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Reliable Computing

An International Journal Devoted to Reliable Mathematical Computations Based on Finite Representations and Guaranteed Accuracy. Edited by Institute of New Technologies in Education St. Petersburg - Moscow

Short Title: Reliab. Comput.
Publisher: Springer, Dordrecht
ISSN: 1385-3139; 1573-1340/e
Online: http://link.springer.com/journal/volumesAndIssues/11155
Predecessor: Interval Computations
Comments: Journal; No longer indexed
Documents Indexed: 408 Publications (1995–2007)
References Indexed: 145 Publications with 2,497 References.
all top 5

Authors

50 Kreinovich, Vladik Yakovlevich
12 Kolev, Lubomir V.
11 Kearfott, Baker
10 Jaulin, Luc
9 Kosheleva, Olga M.
9 Rohn, Jiri
8 Longpré, Luc
7 Berz, Martin
7 Hansen, Eldon Robert
7 Nataraj, Paluri S. V.
7 Neumaier, Arnold
7 Sainz, Miguel Ángel
7 Sharyĭ, Sergeĭ Petrovich
7 Starks, Scott A.
6 Berleant, Daniel J.
6 Garloff, Jürgen
6 Markov, Svetoslav Marinovich
6 Mayer, Günter
6 Nguyen, Hung Trung
6 Wolfe, Michael A.
6 Wolff von Gudenberg, Jürgen
5 Heindl, Gerhard
5 Krämer, Walter
4 Alefeld, Götz E.
4 Dobner, Hans-Jürgen
4 Ferson, Scott A.
4 Hu, Chenyi
4 Lakeyev, Anatoliĭ Valentinovich
4 Makino, Kyoko
4 Nakao, Mitsuhiro T.
4 Ratschek, Helmut
4 Rokne, Jon G.
4 Rump, Siegfried Michael
4 Schulte, Michael J.
4 Vehí, Josep
4 Villaverde, Karen
4 Walster, G. William
4 Xiang, Gang
3 Anguelov, Roumen
3 Ceberio, Martine
3 Csendes, Tibor
3 Ferregut, Carlos
3 Gardeñes, Ernest
3 Ginzburg, Lev R.
3 Hoefkens, Jens
3 Jorba, Lambert
3 Koshelev, Misha
3 Kulpa, Zenon
3 Lang, Bruno
3 Luther, Wolfram Jérôme
3 Menshikov, Gregory G.
3 Muhanna, Rafi L.
3 Nesterov, Vyacheslav M.
3 Oliveira, João Batista
3 Schäfer, Uwe
3 Shen, Zuhe
3 Watanabe, Yoshitaka
3 Yamamoto, Nobito
2 Armengol, Joaquim
2 Arndt, Hans-Robert
2 Baker, Mark Robert
2 Beck, Jan B.
2 Bernat, Andrew
2 Cabrera, Sergio D.
2 Caprani, Ole
2 Chabert, Gilles
2 Claudio, Dalcidio M.
2 de Figueiredo, Luiz Henrique
2 Delanoue, Nicolas
2 Do, Dang-Khoa
2 Dobronets, Boris S.
2 Dyllong, Eva
2 Frommer, Andreas
2 Goldsztejn, Alexandre
2 Granvilliers, Laurent
2 Hajagos, Janos G.
2 Hardouin, Laurent
2 Hofschuster, Werner
2 Hungerbühler, Ralf
2 Ivlev, Ruslan S.
2 Jackson, Kenneth R.
2 Jansson, Christian
2 Kálovics, Ferenc
2 Keller, G. Randy
2 Kohout, Ladislav J.
2 Kotecha, Ketan
2 Kozine, Igor O.
2 Kulisch, Ulrich W.
2 Leclerc, Anthony P.
2 Moore, Ramon E.
2 Mullen, Robert L.
2 Nazarian, Soheil
2 Nedialkov, Nedialko S.
2 Nenov, Ivo P.
2 Ogita, Takeshi
2 Oishi, Shin’ichi
2 Otten, Werner
2 Petković, Ljiljana D.
2 Petković, Miodrag S.
2 Popov, Antony T.
...and 352 more Authors
all top 5

Fields

374 Numerical analysis (65-XX)
43 Operations research, mathematical programming (90-XX)
36 Computer science (68-XX)
22 Statistics (62-XX)
18 General and overarching topics; collections (00-XX)
18 Systems theory; control (93-XX)
17 Linear and multilinear algebra; matrix theory (15-XX)
13 Real functions (26-XX)
12 Ordinary differential equations (34-XX)
11 Probability theory and stochastic processes (60-XX)
9 Field theory and polynomials (12-XX)
9 Functions of a complex variable (30-XX)
8 Approximations and expansions (41-XX)
7 History and biography (01-XX)
7 Partial differential equations (35-XX)
7 Fluid mechanics (76-XX)
7 Biology and other natural sciences (92-XX)
5 Special functions (33-XX)
5 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
4 Mathematical logic and foundations (03-XX)
4 Integral equations (45-XX)
4 Mechanics of particles and systems (70-XX)
4 Mechanics of deformable solids (74-XX)
4 Classical thermodynamics, heat transfer (80-XX)
4 Geophysics (86-XX)
3 Combinatorics (05-XX)
3 Number theory (11-XX)
3 Dynamical systems and ergodic theory (37-XX)
3 Calculus of variations and optimal control; optimization (49-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Algebraic topology (55-XX)
2 Information and communication theory, circuits (94-XX)
1 Algebraic geometry (14-XX)
1 Integral transforms, operational calculus (44-XX)
1 General topology (54-XX)
1 Relativity and gravitational theory (83-XX)

Publications by Year

Citations contained in zbMATH Open

265 Publications have been cited 1,605 times in 1,084 Documents Cited by Year
Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models. Zbl 0976.65061
Berz, Martin; Makino, Kyoko
80
1998
A new technique in systems analysis under interval uncertainty and ambiguity. Zbl 1020.65029
Shary, Sergey P.
73
2002
Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Zbl 1043.60003
Dubois, Didier; Foulloy, Laurent; Mauris, Gilles; Prade, Henri
72
2004
Motivations for an arbitrary precision interval arithmetic and the MPFI library. Zbl 1078.65543
Revol, Nathalie; Rouillier, Fabrice
38
2005
Taylor forms – use and limits. Zbl 1071.65070
Neumaier, Arnold
36
2003
An effective high-order interval method for validating existence and uniqueness of the solution of an IVP for an ODE. Zbl 1003.65077
Nedialkov, Nedialko S.; Jackson, Kenneth R.; Pryce, John D.
32
2001
Interval-valued finite Markov chains. Zbl 1001.65007
Kozine, Igor O.; Utkin, Lev V.
31
2002
Clouds, fuzzy sets, and probability intervals. Zbl 1055.65062
Neumaier, Arnold
28
2004
Computation and application of Taylor polynomials with interval remainder bounds. Zbl 0897.65005
Berz, Martin; Hoffstätter, Georg
27
1998
Linear systems with large uncertainties, with applications to truss structures. Zbl 1117.65063
Neumaier, Arnold; Pownuk, Andrzej
26
2007
Idempotent interval analysis and optimization problems. Zbl 1012.65065
Litvinov, Grigori L.; Sobolevskiĭ, Andrei N.
26
2001
Algebraic approach to the interval linear static identification, tolerance, and control problems, or one more application of Kaucher arithmetic. Zbl 0853.65048
Shary, Sergey P.
25
1996
Efficient control of the dependency problem based on Taylor model methods. Zbl 0936.65073
Makino, Kyoko; Berz, Martin
22
1999
A simple derivation of the Hansen-Bliek-Rohn-Ning-Kearfott enclosure for linear interval equations. Zbl 0936.65055
Neumaier, Arnold
19
1999
Convex imprecise previsions. Zbl 1037.60003
Pelessoni, Renato; Vicig, Paolo
18
2003
Application of interval Newton’s method to chemical engineering problems. Zbl 0838.65058
Balaji, Gopalan V.; Seader, J. D.
18
1995
A method for outer interval solution of linear parametric systems. Zbl 1055.65045
Kolev, Lubomir V.
18
2004
Exact bounds on finite populations of interval data. Zbl 1076.65013
Ferson, Scott; Ginzburg, Lev; Kreinovich, Vladik; Longpré, Luc; Aviles, Monica
18
2005
A method for outer interval solution of systems of linear equations depending linearly on interval parameters. Zbl 1085.65039
Skalna, Iwona
17
2006
Algebraic approach in the “outer problem” for interval linear equations. Zbl 0881.65024
Shary, Sergey P.
16
1997
Interval finite elements as a basis for generalized models of uncertainty in engineering mechanics. Zbl 1206.74021
Muhanna, Rafi L.; Zhang, Hao; Mullen, Robert L.
15
2007
A right-preconditioning process for the formal-algebraic approach to inner and outer estimation of AE-solution sets. Zbl 1081.65041
Goldsztejn, Alexandre
15
2005
A note on epsilon-inflation. Zbl 0920.65031
Rump, Siegfried M.
15
1998
Modal intervals. Zbl 0982.65060
Gardeñes, Ernest; Sainz, Miguel Á.; Jorba, Lambert; Calm, Remei; Estela, Rosa; Mielgo, Honorino; Trepat, Albert
14
2001
Sharpness in interval computations. Zbl 0881.65032
Hansen, Eldon R.
14
1997
A quasi-metric topology compatible with inclusion monotonicity on interval space. Zbl 0889.65051
Acióly, Benedito Melo; Bedregal, Benjamín R. Callejas
14
1997
On interval systems \([x] = [A][x] + [b]\) and the powers of interval matrices in complex interval arithmetics. Zbl 1115.65033
Arndt, Hans-Robert
13
2007
Automatic computation of a linear interval enclosure. Zbl 0979.65041
Kolev, Lubomir V.
13
2001
Exact Minkowski products of \(N\) complex disks. Zbl 1028.65048
Farouki, Rida T.; Pottmann, Helmut
13
2002
New methods for high-dimensional verified quadrature. Zbl 0947.65026
Berz, Martin; Makino, Kyoko
13
1999
Towards combining probabilistic and interval uncertainty in engineering calculations: algorithms for computing statistics under interval uncertainty, and their computational complexity. Zbl 1104.65010
Kreinovich, Vladik; Xiang, Gang; Starks, Scott A.; Longpré, Luc; Ceberio, Martine; Araiza, Roberto; Beck, Jan; Kandathi, Raj; Nayak, Asis; Torres, Roberto; Hajagos, Janos G.
13
2006
Use of interval slopes for the irrational part of factorable functions. Zbl 0878.65036
Kolev, Lubomir V.
13
1997
An application of interval methods to stock market forecasting. Zbl 1125.91348
Hu, Chenyi; He, Ling T.
12
2007
Solutions for the portfolio selection problem with interval and fuzzy coefficients. Zbl 1087.91026
Ida, Masaaki
12
2004
Empirical investigation of the convergence speed of inclusion functions in a global otimization context. Zbl 1078.65547
Tóth, Boglárka; Csendes, Tibor
12
2005
Outer interval solution of the eigenvalue problem under general form parametric dependencies. Zbl 1085.65032
Kolev, Lubomir V.
12
2006
Worst-case simulation of discrete linear time-invariant interval dynamic systems. Zbl 1079.65128
Puig, Vicenç; Saludes, Jordi; Quevedo, Joseba
12
2003
Bounding the results of arithmetic operations on random variables of unknown dependency using intervals. Zbl 0908.65139
Berleant, Daniel; Goodman-Strauss, Chaim
11
1998
Enclosing solutions of overdetermined systems of linear interval equations. Zbl 0855.65037
Rohn, Jiří
11
1996
The set of Hausdorff continuous functions – the largest linear space of interval functions. Zbl 1110.65036
Anguelov, Roumen; Markov, Svetoslav; Sendov, Blagovest
11
2006
Complexity of some linear problems with interval data. Zbl 0888.65052
Rohn, Jiří
11
1997
Robust autonomous robot localization using interval analysis. Zbl 0978.70004
Kieffer, Michel; Jaulin, Luc; Walter, Éric; Meizel, Dominique
10
2000
Multiplication distributivity of proper and improper intervals. Zbl 0978.65040
Popova, Evgenija D.
10
2001
An interval Hermite-Obreschkoff method for computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation. Zbl 0947.65081
Nedialkov, Nedialko S.; Jackson, Kenneth R.
10
1999
Statool: A tool for distribution envelope determination (DEnv), an interval-based algorithm for arithmetic on random variables. Zbl 1020.65010
Berleant, Daniel; Xie, Lizhi; Zhang, Jianzhong
10
2003
Quantified set inversion algorithm with applications to control. Zbl 1081.65519
Herrero, Pau; Sainz, Miguel A.; Vehí, Josep; Jaulin, Luc
9
2005
Computation of bounds on population parameters when the data are incomplete. Zbl 1140.62314
Horowitz, Joel L.; Manski, Charles F.; Ponomareva, Maria; Stoye, Jörg
8
2003
Tree-based credal networks for classification. Zbl 1038.62030
Zaffalon, Marco; Fagiuoli, Enrico
8
2003
On the algebraic properties of intervals and some applications. Zbl 0978.65039
Markov, Svetoslav
8
2001
On the applicability of the interval Gaussian algorithm. Zbl 0933.65027
Mayer, Günter; Rohn, Jiří
8
1998
Verified high-order inversion of functional dependencies and interval Newton methods. Zbl 1016.65030
Berz, Martin; Hoefkens, Jens
8
2001
Complex interval arithmetic using polar form. Zbl 1088.65042
Candau, Yves; Raissi, Tarek; Ramdani, Nacim; Ibos, Laurent
8
2006
A new method for global solution of systems of nonlinear equations. Zbl 1005.65047
Kolev, Lubomir V.
7
1998
Inner estimation of the united solution set of interval linear algebraic system. Zbl 0844.65037
Kupriyanova, Ludmila
7
1995
Interval Gauss-Seidel method for generalized solution sets to interval linear systems. Zbl 0976.65032
Shary, Sergey P.
7
2001
Approximate quantified constraint solving by cylindrical box decomposition. Zbl 0997.65077
Ratschan, Stefan
7
2002
Sharp bounds on interval polynomial roots. Zbl 0994.65053
Hansen, Eldon R.; Walster, G. William
7
2002
Interval Householder method for complex linear systems. Zbl 1088.65024
Djanybekov, Bakyt S.
7
2006
Enclosing solutions of linear complementarity problems for H-matrices. Zbl 1074.65066
Alefeld, Götz; Wang, Zhengyu; Shen, Zuhe
7
2004
Ostrowski-like method with corrections for the inclusion of polynomial zeros. Zbl 1075.65070
Petković, Miodrag S.; Milošević, Dušan M.
7
2004
Using zonotopes for overestimation-free interval least-squares – some geodetic applications. Zbl 1073.65034
Schön, Steffen; Kutterer, Hansjörg
7
2005
Controlling the wrapping effect in the solution of ODEs for asteroids. Zbl 1219.70003
Hoefkens, Jens; Berz, Martin; Makino, Kyoko
7
2003
Solution set characterization of linear interval systems with a specific dependence structure. Zbl 1127.65024
Hladík, Milan
6
2007
Finding all solutions of nonlinear equations using linear combinations of functions. Zbl 0958.65060
Yamamura, Kiyotaka
6
2000
Application of Bernstein expansion to the solution of control problems. Zbl 0965.65095
Garloff, Jürgen
6
2000
Optimal finite characterization of linear problems with inexact data. Zbl 1080.15002
Kreinovich, Vladik
6
2005
On bounding solutions of underdetermined systems. Zbl 0990.65057
Wolfe, Michael A.
6
2001
Global optimization with higher order inclusion function forms. I: A combined Taylor-Bernstein form. Zbl 1038.65052
Nataraj, Paluri S. V.; Kotecha, Ketan
6
2004
A general reliable quadratic form: An extension of affine arithmetic. Zbl 1106.65042
Messine, Frédéric; Touhami, Ahmed
6
2006
Monte-Carlo-type techniques for processing interval uncertainty, and their potential engineering applications. Zbl 1106.65043
Kreinovich, Vladik; Beck, Jan; Ferregut, Carlos; Sanchez, Araceli; Keller, G. Randy; Averill, Matthew; Starks, Scott A.
6
2007
Enclosing solutions of singular interval systems iteratively. Zbl 1079.65027
Alefeld, Götz; Mayer, Günter
6
2005
Fast inclusion of interval matrix multiplication. Zbl 1072.65063
Ogita, Takeshi; Oishi, Shin’ichi
6
2005
A contribution to the feasibility of the interval Gaussian algorithm. Zbl 1086.65023
Mayer, Günter
6
2006
Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations. Zbl 1029.65045
Ogita, Takeshi; Oishi, Shin’ichi; Ushiro, Yasunori
6
2003
Some computer assisted proofs for solutions of the heat convection problems. Zbl 1126.35352
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito; Nishida, Takaaki
6
2003
On fitting empirical data under interval error. Zbl 1081.65503
Zhilin, Sergei I.
5
2005
A combined method for enclosing all solutions of nonlinear systems of polynomial equations. Zbl 0833.65046
Jäger, Christine; Ratz, Dietmar
5
1995
Numerical computation of the least common multiple of a set of polynomials. Zbl 0984.65016
Karcanias, Nicos; Mitrouli, Marilena
5
2000
On factorization of analytic functions and its verification. Zbl 0986.65053
Sakurai, Tetsuya; Sugiura, Hiroshi
5
2000
Reliable minimax parameter estimation. Zbl 0987.65011
Jaulin, Luc
5
2001
Removing degeneracies by perturbing the problem or perturbing the world. Zbl 0996.65019
Alliez, Pierre; Devillers, Olivier; Snoeyink, Jack
5
2000
Linear interval tolerance problem and linear programming techniques. Zbl 1003.65061
Beaumont, Oliver; Philippe, Bernard
5
2001
Using Pearson correlation to improve envelopes around the distributions of functions. Zbl 1036.60010
Berleant, Daniel; Zhang, Jianzhong
5
2004
Slope intervals, generalized gradients, semigradients, slant derivatives, and csets. Zbl 1072.65094
Muñoz, Humberto; Kearfott, R. Baker
5
2004
Improvement of a direct method for outer solution of linear parametric systems. Zbl 1094.65022
Kolev, Lubomir V.
5
2006
Computational experience with rigorous error bounds for the Netlib linear programming library. Zbl 1099.65051
Keil, Christian; Jansson, Christian
5
2006
Parameter reconstruction for biochemical networks using interval analysis. Zbl 1098.65082
Tucker, Warwick; Moulton, Vincent
5
2006
Outlier detection under interval uncertainty: algorithmic solvability and computational complexity. Zbl 1076.65014
Kreinovich, Vladik; Longpré, Luc; Patangay, Praveen; Ferson, Scott; Ginzburg, Lev
5
2005
On the proofs of some statements concerning the theorems of Kantorovich, Moore, and Miranda. Zbl 1077.65052
Schnurr, Marco
5
2005
Diagramming representation of interval space in proving theorems about interval relations. Zbl 0888.65055
Kulpa, Zenon
5
1997
Two adaptive Gauss-Legendre type algorithms for the verified computation of definite integrals. Zbl 0858.65020
Krämer, Walter; Wedner, Stefan
5
1996
Outer solution of linear systems whose elements are affine functions of interval parameters. Zbl 1024.65027
Kolev, Lubomir V.
5
2002
Estimating and validating the cumulative distribution of a function of random variables: Toward the development of distribution arithmetic. Zbl 1020.65008
Lodwick, Weldon A.; Jamison, K. David
5
2003
Bounds on generalized linear predictors with incomplete outcome data. Zbl 1120.65007
Stoye, Jörg
4
2007
Computing population variance and entropy under interval uncertainty: Linear-time algorithms. Zbl 1146.65014
Xiang, Gang; Ceberio, Martine; Kreinovich, Vladik
4
2007
Dependable handling of uncertainty. Zbl 1140.62301
Berleant, Daniel; Cheong, Mei-Peng; Chu, Chris; Guan, Yong; Kamal, Ahmed; Sheblé, Gerald; Ferson, Scott; Peters, James F.
4
2003
Why intervals? A simple limit theorem that is similar to limit theorems from statistics. Zbl 0831.65053
Kreinovich, Vladik
4
1995
An automatic and guaranteed determination of the number of roots of an analytic function interior to a simple closed curve in the complex plane. Zbl 0840.65013
Herlocker, Jonathan; Ely, Jeffrey
4
1995
Path planning using intervals and graphs. Zbl 1021.65029
Jaulin, Luc
4
2001
Interval methods in non-destructive testing of material structures. Zbl 1045.65043
Worden, Keith; Osegueda, Roberto; Ferregut, Carlos; Nazarian, Soheil; George, Debra L.; George, Mary J.; Kreinovich, Vladik; Kosheleva, Olga; Cabrera, Sergio
4
2001
Linear systems with large uncertainties, with applications to truss structures. Zbl 1117.65063
Neumaier, Arnold; Pownuk, Andrzej
26
2007
Interval finite elements as a basis for generalized models of uncertainty in engineering mechanics. Zbl 1206.74021
Muhanna, Rafi L.; Zhang, Hao; Mullen, Robert L.
15
2007
On interval systems \([x] = [A][x] + [b]\) and the powers of interval matrices in complex interval arithmetics. Zbl 1115.65033
Arndt, Hans-Robert
13
2007
An application of interval methods to stock market forecasting. Zbl 1125.91348
Hu, Chenyi; He, Ling T.
12
2007
Solution set characterization of linear interval systems with a specific dependence structure. Zbl 1127.65024
Hladík, Milan
6
2007
Monte-Carlo-type techniques for processing interval uncertainty, and their potential engineering applications. Zbl 1106.65043
Kreinovich, Vladik; Beck, Jan; Ferregut, Carlos; Sanchez, Araceli; Keller, G. Randy; Averill, Matthew; Starks, Scott A.
6
2007
Bounds on generalized linear predictors with incomplete outcome data. Zbl 1120.65007
Stoye, Jörg
4
2007
Computing population variance and entropy under interval uncertainty: Linear-time algorithms. Zbl 1146.65014
Xiang, Gang; Ceberio, Martine; Kreinovich, Vladik
4
2007
Formulation for reliable analysis of structural frames. Zbl 1106.74040
Corliss, George; Foley, Christopher; Kearfott, R. Baker
3
2007
A new robust algorithm to trace curves. Zbl 1120.65016
Faudot, Dominique; Michelucci, Dominique
3
2007
On sufficient conditions of the injectivity: Development of a numerical test algorithm via interval analysis. Zbl 1126.65041
Lagrange, Sébastien; Delanoue, Nicolas; Jaulin, Luc
3
2007
Computing the pessimism of inclusion functions. Zbl 1154.65031
Chabert, Gilles; Jaulin, Luc
2
2007
Determining the positive definiteness margin of interval matrices. Zbl 1154.65025
Kolev, Lubomir V.
2
2007
Guaranteeing the homotopy type of a set defined by non-linear inequalities. Zbl 1126.65040
Delanoue, Nicolas; Jaulin, Luc; Cottenceau, Bertrand
2
2007
Requirements analysis for engineering computation: a systematic approach for improving reliability. Zbl 1106.68348
Smith, Spencer; Lai, Lei; Khedri, Ridha
2
2007
Solving interval constraints by linearization in computer-aided design. Zbl 1110.65018
Wang, Yan; Nnaji, Bartholomew O.
1
2007
Unimodality, independence lead to NP-hardness of interval probability problems. Zbl 1120.65006
Berleant, Daniel J.; Kosheleva, Olga; Kreinovich, Vladik; Nguyen, Hung T.
1
2007
Guaranteed parameter set estimation for exponential sums: the three-terms case. Zbl 1120.65077
Garloff, Jürgen; Idriss, Ismail; Smith, Andrew P.
1
2007
Optimal multiplication of \(G\)-intervals. Zbl 1139.65035
Kolev, Lubomir V.
1
2007
Interval Monte Carlo as an alternative to second-order sampling for estimating ecological risk. Zbl 1102.92053
Hajagos, Janos G.
1
2007
Experiments with range computations using extrapolation. Zbl 1108.65044
Paluri, Nataraj S. V.; Sondur, Shanta
1
2007
A method for outer interval solution of systems of linear equations depending linearly on interval parameters. Zbl 1085.65039
Skalna, Iwona
17
2006
Towards combining probabilistic and interval uncertainty in engineering calculations: algorithms for computing statistics under interval uncertainty, and their computational complexity. Zbl 1104.65010
Kreinovich, Vladik; Xiang, Gang; Starks, Scott A.; Longpré, Luc; Ceberio, Martine; Araiza, Roberto; Beck, Jan; Kandathi, Raj; Nayak, Asis; Torres, Roberto; Hajagos, Janos G.
13
2006
Outer interval solution of the eigenvalue problem under general form parametric dependencies. Zbl 1085.65032
Kolev, Lubomir V.
12
2006
The set of Hausdorff continuous functions – the largest linear space of interval functions. Zbl 1110.65036
Anguelov, Roumen; Markov, Svetoslav; Sendov, Blagovest
11
2006
Complex interval arithmetic using polar form. Zbl 1088.65042
Candau, Yves; Raissi, Tarek; Ramdani, Nacim; Ibos, Laurent
8
2006
Interval Householder method for complex linear systems. Zbl 1088.65024
Djanybekov, Bakyt S.
7
2006
A general reliable quadratic form: An extension of affine arithmetic. Zbl 1106.65042
Messine, Frédéric; Touhami, Ahmed
6
2006
A contribution to the feasibility of the interval Gaussian algorithm. Zbl 1086.65023
Mayer, Günter
6
2006
Improvement of a direct method for outer solution of linear parametric systems. Zbl 1094.65022
Kolev, Lubomir V.
5
2006
Computational experience with rigorous error bounds for the Netlib linear programming library. Zbl 1099.65051
Keil, Christian; Jansson, Christian
5
2006
Parameter reconstruction for biochemical networks using interval analysis. Zbl 1098.65082
Tucker, Warwick; Moulton, Vincent
5
2006
Fast algorithm for computing the upper endpoint of sample variance for interval data: Case of sufficiently accurate measurements. Zbl 1088.65008
Xiang, Gang
3
2006
Population variance under interval uncertainty: a new algorithm. Zbl 1098.65006
Dantsin, Evgeny; Kreinovich, Vladik; Wolpert, Alexander; Xiang, Gang
3
2006
Regularity of interval matrices and theorems of the alternatives. Zbl 1090.15004
Rohn, Jiří
3
2006
Hardware support for interval arithmetic. Zbl 1092.65040
Kirchner, Reinhard; Kulisch, Ulrich W.
2
2006
Solving overdetermined systems of interval linear equations. Zbl 1092.65034
Hansen, Eldon; Walster, G. William
2
2006
Analysis and design of robust controllers using the interval Diophantine equation. Zbl 1098.65077
Lordelo, Alfredo D. S.; Juzzo, Edvaldo A.; Ferreira, Paulo A. V.
2
2006
Uncertainty in thermal basin modeling: an interval finite element approach. Zbl 1104.65093
Pereira, Sebastião C.; Mello, Ulisses T.; Ebecken, Nelson F. F.; Muhanna, Rafi L.
2
2006
Efficient task scheduling in the parallel result-verifying solution of nonlinear systems. Zbl 1083.65051
Beelitz, Thomas; Lang, Bruno; Bischof, Christian H.
2
2006
Sharpening interval computations. Zbl 1088.65025
Hansen, Eldon
1
2006
Robust control for two-time-scale discrete interval systems. Zbl 1102.65074
Patre, Balasaheb M.; Bandyopadhyay, Bijnan
1
2006
New formulae for multiplication of intervals. Zbl 1129.65034
Kolev, Lubomir V.
1
2006
Towards optimal use of multi-precision arithmetic: a remark. Zbl 1098.65046
Kreinovich, Vladik; Rump, Siegfried
1
2006
Special issue: Reliability engineering computing. Papers based on the presentations at the workshop, Savannah, GA, USA, September 2004. Zbl 1109.65304
1
2006
Introductory remarks on reliable engineering computing. Zbl 1198.65087
Moore, Ramon E.
1
2006
Reliable modeling and optimization for chemical engineering applications: Interval analysis approach. Zbl 1104.65057
Lin, Youdong; Gwaltney, C. Ryan; Stadtherr, Mark A.
1
2006
Motivations for an arbitrary precision interval arithmetic and the MPFI library. Zbl 1078.65543
Revol, Nathalie; Rouillier, Fabrice
38
2005
Exact bounds on finite populations of interval data. Zbl 1076.65013
Ferson, Scott; Ginzburg, Lev; Kreinovich, Vladik; Longpré, Luc; Aviles, Monica
18
2005
A right-preconditioning process for the formal-algebraic approach to inner and outer estimation of AE-solution sets. Zbl 1081.65041
Goldsztejn, Alexandre
15
2005
Empirical investigation of the convergence speed of inclusion functions in a global otimization context. Zbl 1078.65547
Tóth, Boglárka; Csendes, Tibor
12
2005
Quantified set inversion algorithm with applications to control. Zbl 1081.65519
Herrero, Pau; Sainz, Miguel A.; Vehí, Josep; Jaulin, Luc
9
2005
Using zonotopes for overestimation-free interval least-squares – some geodetic applications. Zbl 1073.65034
Schön, Steffen; Kutterer, Hansjörg
7
2005
Optimal finite characterization of linear problems with inexact data. Zbl 1080.15002
Kreinovich, Vladik
6
2005
Enclosing solutions of singular interval systems iteratively. Zbl 1079.65027
Alefeld, Götz; Mayer, Günter
6
2005
Fast inclusion of interval matrix multiplication. Zbl 1072.65063
Ogita, Takeshi; Oishi, Shin’ichi
6
2005
On fitting empirical data under interval error. Zbl 1081.65503
Zhilin, Sergei I.
5
2005
Outlier detection under interval uncertainty: algorithmic solvability and computational complexity. Zbl 1076.65014
Kreinovich, Vladik; Longpré, Luc; Patangay, Praveen; Ferson, Scott; Ginzburg, Lev
5
2005
On the proofs of some statements concerning the theorems of Kantorovich, Moore, and Miranda. Zbl 1077.65052
Schnurr, Marco
5
2005
Contracting optimally an interval matrix without loosing any positive semi-definite matrix is a tractable problem. Zbl 1076.65041
Jaulin, Luc; Henrion, Didier
4
2005
Computing system reliability given interval-valued characteristics of the components. Zbl 1075.65086
Utkin, Lev V.; Kozine, Igor O.
4
2005
A theorem on regularity of interval matrices. Zbl 1080.15003
Hansen, Eldon
3
2005
Interval-affine Gaussian algorthm for constrained systems. Zbl 1081.65506
Akhmerov, Ramil R.
3
2005
On unbounded tolerable solution sets. Zbl 1082.15006
Sharaya, Irene A.
2
2005
On the solutions of the interval system \([x] = [a][x] + [b]\). Zbl 1074.65049
Arndt, Hans-Robert; Mayer, Günter
2
2005
Tolerances in geometric constraint problems. Zbl 1075.65025
Wallner, Johannes; Schröcker, Hans-Peter; Hu, Shi-Min
2
2005
How strong is strong regularity? Zbl 1080.15005
Rohn, Jiří
1
2005
Interval mathematical library based on Chebyshev and Taylor series expansion. Zbl 1081.65518
Ershov, Alexei G.; Kashevarova, Tamara P.
1
2005
The optimal solution of an interval system of linear algebraic equations. Zbl 1075.65061
Lyashko, Marina
1
2005
Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Zbl 1043.60003
Dubois, Didier; Foulloy, Laurent; Mauris, Gilles; Prade, Henri
72
2004
Clouds, fuzzy sets, and probability intervals. Zbl 1055.65062
Neumaier, Arnold
28
2004
A method for outer interval solution of linear parametric systems. Zbl 1055.65045
Kolev, Lubomir V.
18
2004
Solutions for the portfolio selection problem with interval and fuzzy coefficients. Zbl 1087.91026
Ida, Masaaki
12
2004
Enclosing solutions of linear complementarity problems for H-matrices. Zbl 1074.65066
Alefeld, Götz; Wang, Zhengyu; Shen, Zuhe
7
2004
Ostrowski-like method with corrections for the inclusion of polynomial zeros. Zbl 1075.65070
Petković, Miodrag S.; Milošević, Dušan M.
7
2004
Global optimization with higher order inclusion function forms. I: A combined Taylor-Bernstein form. Zbl 1038.65052
Nataraj, Paluri S. V.; Kotecha, Ketan
6
2004
Using Pearson correlation to improve envelopes around the distributions of functions. Zbl 1036.60010
Berleant, Daniel; Zhang, Jianzhong
5
2004
Slope intervals, generalized gradients, semigradients, slant derivatives, and csets. Zbl 1072.65094
Muñoz, Humberto; Kearfott, R. Baker
5
2004
Fuzzy linear programming with interactive uncertain parameters. Zbl 1048.65062
Inuiguchi, Masahiro; Tanino, Tetsuzo
4
2004
Set computation for nonlinear control. Zbl 1040.93045
Jaulin, Luc; Ratschan, Stefan; Hardouin, Laurent
3
2004
Characterization of interval fuzzy logic systems of connectives by group transformations. Zbl 1055.03016
Kohout, Ladislav J.; Kim, Eunjin
3
2004
Modeling uncertain sparse data with fuzzy B-splines. Zbl 1048.65015
Anile, Angelo Marcello; Spinella, Salvatore
3
2004
On the use of random set theory to bracket the results of Monte Carlo simulations. Zbl 1038.65044
Tonon, Fulvio
2
2004
On a refined analysis of some problems in interval arithmetic using real number complexity theory. Zbl 1055.65061
Meer, Klaus
2
2004
Dirty pages of logarithm tables, lifetime of the universe, and (subjective) probabilities on finite and infinite intervals. Zbl 1045.65042
Nguyen, Hung T.; Kreinovich, Vladik; Longpré, Luc
1
2004
On the significance of digits in interval notation. Zbl 1038.65043
Van Emden, Maarten H.
1
2004
Application of functional intervals to the response evaluation of linear time-invariant systems with fuzzy input. Zbl 1070.93029
Bondia, Jorge; Picó, Jesús
1
2004
Eliminating duplicates under interval and fuzzy uncertainty: an asymptotically optimal algorithm and its geospatial applications. Zbl 1088.68585
Torres, Roberto; Keller, G. Randy; Kreinovich, Vladik; Longpré, Luc; Starks, Scott A.
1
2004
Taylor forms – use and limits. Zbl 1071.65070
Neumaier, Arnold
36
2003
Convex imprecise previsions. Zbl 1037.60003
Pelessoni, Renato; Vicig, Paolo
18
2003
Worst-case simulation of discrete linear time-invariant interval dynamic systems. Zbl 1079.65128
Puig, Vicenç; Saludes, Jordi; Quevedo, Joseba
12
2003
Statool: A tool for distribution envelope determination (DEnv), an interval-based algorithm for arithmetic on random variables. Zbl 1020.65010
Berleant, Daniel; Xie, Lizhi; Zhang, Jianzhong
10
2003
Computation of bounds on population parameters when the data are incomplete. Zbl 1140.62314
Horowitz, Joel L.; Manski, Charles F.; Ponomareva, Maria; Stoye, Jörg
8
2003
Tree-based credal networks for classification. Zbl 1038.62030
Zaffalon, Marco; Fagiuoli, Enrico
8
2003
Controlling the wrapping effect in the solution of ODEs for asteroids. Zbl 1219.70003
Hoefkens, Jens; Berz, Martin; Makino, Kyoko
7
2003
Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations. Zbl 1029.65045
Ogita, Takeshi; Oishi, Shin’ichi; Ushiro, Yasunori
6
2003
Some computer assisted proofs for solutions of the heat convection problems. Zbl 1126.35352
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito; Nishida, Takaaki
6
2003
Estimating and validating the cumulative distribution of a function of random variables: Toward the development of distribution arithmetic. Zbl 1020.65008
Lodwick, Weldon A.; Jamison, K. David
5
2003
Dependable handling of uncertainty. Zbl 1140.62301
Berleant, Daniel; Cheong, Mei-Peng; Chu, Chris; Guan, Yong; Kamal, Ahmed; Sheblé, Gerald; Ferson, Scott; Peters, James F.
4
2003
Robust approximation of offsets, bisectors, and medial axes of plane curves. Zbl 1019.65019
Oliveira, João Batista; De Figueiredo, Luiz Henrique
3
2003
...and 165 more Documents
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Cited by 1,510 Authors

36 Hladík, Milan
30 Kreinovich, Vladik Yakovlevich
29 Jaulin, Luc
15 Miyajima, Shinya
13 Dubois, Didier
13 Popova, Evgeniya D.
12 Bedregal, Benjamín René Callejas
11 Sharyĭ, Sergeĭ Petrovich
11 Skalna, Iwona
11 Vicig, Paolo
10 Goldsztejn, Alexandre
10 Xiang, Gang
9 Dimuro, Graçaliz Pereira
9 Ferson, Scott A.
9 Kolev, Lubomir V.
9 Mireles-James, Jason D.
9 Neumaier, Arnold
9 Pelessoni, Renato
8 Behl, Ramandeep
8 Chachuat, Benoît
8 Dehghani-Madiseh, Marzieh
8 Gazdag-Tóth, Boglárka
8 Lessard, Jean-Philippe
8 Li, Haohao
8 Li, Wei
8 Myšková, Helena
8 Nakao, Mitsuhiro T.
8 Ogita, Takeshi
8 Oishi, Shin’ichi
8 Prade, Henri M.
8 Ramdani, Nacim
7 Černý, Michal
7 Chakraverty, Snehashish
7 Farouki, Rida T.
7 Hardouin, Laurent
7 Mayer, Günter
7 Messine, Frédéric
7 Plavka, Ján
7 Puig, Vicenç
7 Rauh, Andreas
7 Rump, Siegfried Michael
7 Strauss, Olivier
6 Alefeld, Götz E.
6 Alshomrani, Ali Saleh
6 Dehghan Takht Fooladi, Mehdi
6 Fernandez Hernandez, Jose
6 Ghanbari, Mojtaba
6 Jiang, Chao
6 Kieffer, Michel
6 Longpré, Luc
6 Nataraj, Paluri S. V.
6 Reiser, Renata Hax Sander
6 Rohn, Jiri
6 Škulj, Damjan
6 Starks, Scott A.
6 Walter, Eric
6 Watanabe, Yoshitaka
6 Wilczak, Daniel
6 Xia, Mengxue
6 Yamamura, Kiyotaka
5 Barton, Paul I.
5 Behera, Diptiranjan
5 Berz, Martin
5 Bünger, Florian
5 Ceberio, Martine
5 Cottenceau, Bertrand
5 Hashemi, Behnam
5 Jankowska, Malgorzata A.
5 Kearfott, Baker
5 Lodwick, Weldon Alexander
5 Luther, Wolfram Jérôme
5 Milošević, Dušan M.
5 Nedialkov, Nedialko S.
5 Ninin, Jordan
5 Ozaki, Katsuhisa
5 Petković, Miodrag S.
5 Santiago, Regivan H. Nunes
5 Schichl, Hermann
5 Wang, Chong
5 Wang, Zhengyu
5 Zgliczyński, Piotr
4 Allahviranloo, Tofigh
4 Argyros, Ioannis Konstantinos
4 Armellin, Roberto
4 Auer, Ekaterina
4 Chabert, Gilles
4 Combastel, Christophe
4 Cordero, Alicia
4 Farjudian, Amin
4 Frommer, Andreas
4 Herrero, Pau
4 Hofer, Eberhard P.
4 Houska, Boris
4 Jermann, Christophe
4 Karcanias, Nicos
4 Kerre, Etienne E.
4 Lhommeau, Mehdi
4 Luo, Jiajia
4 Magreñán, Ángel Alberto
4 Makino, Kyoko
...and 1,410 more Authors
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Cited in 234 Journals

63 International Journal of Approximate Reasoning
62 Journal of Computational and Applied Mathematics
60 Reliable Computing
54 Fuzzy Sets and Systems
43 Applied Mathematics and Computation
39 Linear Algebra and its Applications
32 Journal of Global Optimization
22 Information Sciences
17 Numerical Algorithms
16 Computers & Mathematics with Applications
16 Automatica
16 Soft Computing
14 Computing
13 Applied Mathematical Modelling
12 International Journal of Applied Mathematics and Computer Science
11 Computer Methods in Applied Mechanics and Engineering
10 Linear and Multilinear Algebra
10 International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
10 Mathematics in Computer Science
10 Optimization Letters
9 BIT
9 Japan Journal of Industrial and Applied Mathematics
9 Communications in Nonlinear Science and Numerical Simulation
8 Journal of Symbolic Computation
8 Constraints
7 Artificial Intelligence
7 International Journal of General Systems
7 Journal of Mathematical Analysis and Applications
7 Applied Numerical Mathematics
7 European Journal of Operational Research
7 Journal of Mathematical Chemistry
6 International Journal of Control
6 International Journal of Adaptive Control and Signal Processing
6 ELA. The Electronic Journal of Linear Algebra
6 Mathematical Problems in Engineering
6 Journal of Statistical Theory and Practice
5 Kybernetika
5 Theoretical Computer Science
5 Discrete & Computational Geometry
5 Journal of Automated Reasoning
5 International Journal of Computer Mathematics
5 Computational Statistics and Data Analysis
5 Computational Optimization and Applications
5 Computational and Applied Mathematics
5 Optimization Methods & Software
5 SIAM Journal on Applied Dynamical Systems
5 Nonlinear Analysis. Hybrid Systems
4 Mathematics of Computation
4 International Journal for Numerical Methods in Engineering
4 Journal of Differential Equations
4 Mathematics and Computers in Simulation
4 Numerische Mathematik
4 Annals of Operations Research
4 Computational Geometry
4 Discrete Event Dynamic Systems
4 Mathematical Programming. Series A. Series B
4 Celestial Mechanics and Dynamical Astronomy
4 Journal of Nonlinear Science
4 The Journal of Logic and Algebraic Programming
4 Foundations of Computational Mathematics
4 International Journal of Systems Science. Principles and Applications of Systems and Integration
3 Discrete Applied Mathematics
3 Journal of Optimization Theory and Applications
3 Numerical Functional Analysis and Optimization
3 Opsearch
3 Systems & Control Letters
3 Computer Aided Geometric Design
3 Optimization
3 Applied Mathematics Letters
3 Mathematical and Computer Modelling
3 International Journal of Computational Geometry & Applications
3 Journal of Dynamics and Differential Equations
3 Journal of Computer and Systems Sciences International
3 Annals of Mathematics and Artificial Intelligence
3 Differential Equations
3 Journal of Intelligent and Fuzzy Systems
3 Acta Mechanica Sinica
3 Symmetry
3 International Journal of Applied and Computational Mathematics
2 Acta Mechanica
2 Information Processing Letters
2 Nonlinearity
2 The Mathematical Intelligencer
2 Journal of Econometrics
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Insurance Mathematics & Economics
2 Applied Mathematics and Mechanics. (English Edition)
2 Computers & Operations Research
2 COMPEL
2 Neural Networks
2 MSCS. Mathematical Structures in Computer Science
2 Applications of Mathematics
2 Computational Statistics
2 Journal of Statistical Computation and Simulation
2 Indagationes Mathematicae. New Series
2 Journal of Mathematical Imaging and Vision
2 Advances in Engineering Software
2 Applied Mathematics. Series B (English Edition)
2 Numerical Linear Algebra with Applications
2 Advances in Computational Mathematics
...and 134 more Journals
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Cited in 54 Fields

537 Numerical analysis (65-XX)
202 Computer science (68-XX)
176 Operations research, mathematical programming (90-XX)
127 Linear and multilinear algebra; matrix theory (15-XX)
107 Systems theory; control (93-XX)
98 Statistics (62-XX)
53 Probability theory and stochastic processes (60-XX)
50 Mathematical logic and foundations (03-XX)
47 Ordinary differential equations (34-XX)
47 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
37 Dynamical systems and ergodic theory (37-XX)
37 Mechanics of deformable solids (74-XX)
28 Partial differential equations (35-XX)
25 Mechanics of particles and systems (70-XX)
19 Calculus of variations and optimal control; optimization (49-XX)
18 Biology and other natural sciences (92-XX)
17 Approximations and expansions (41-XX)
16 Real functions (26-XX)
16 Information and communication theory, circuits (94-XX)
15 Fluid mechanics (76-XX)
13 Order, lattices, ordered algebraic structures (06-XX)
13 Functions of a complex variable (30-XX)
12 Convex and discrete geometry (52-XX)
9 Number theory (11-XX)
9 Commutative algebra (13-XX)
9 Operator theory (47-XX)
8 Field theory and polynomials (12-XX)
8 Algebraic geometry (14-XX)
8 Measure and integration (28-XX)
7 Integral equations (45-XX)
7 Functional analysis (46-XX)
7 Geometry (51-XX)
7 General topology (54-XX)
6 Combinatorics (05-XX)
6 General algebraic systems (08-XX)
6 Geophysics (86-XX)
5 Associative rings and algebras (16-XX)
4 Special functions (33-XX)
4 Classical thermodynamics, heat transfer (80-XX)
3 Integral transforms, operational calculus (44-XX)
3 Optics, electromagnetic theory (78-XX)
3 Quantum theory (81-XX)
3 Statistical mechanics, structure of matter (82-XX)
2 General and overarching topics; collections (00-XX)
2 Group theory and generalizations (20-XX)
2 Difference and functional equations (39-XX)
2 Differential geometry (53-XX)
2 Global analysis, analysis on manifolds (58-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Sequences, series, summability (40-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Algebraic topology (55-XX)
1 Manifolds and cell complexes (57-XX)
1 Astronomy and astrophysics (85-XX)

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