Reliable ComputingAn 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 Latest Issues 13, No. 6 (2007) 13, No. 5 (2007) 13, No. 4 (2007) 13, No. 3 (2007) 13, No. 2 (2007) 13, No. 1 (2007) 12, No. 6 (2006) 12, No. 5 (2006) 12, No. 4 (2006) 12, No. 3 (2006) 12, No. 2 (2006) 12, No. 1 (2006) 11, No. 6 (2005) 11, No. 5 (2005) 11, No. 4 (2005) 11, No. 3 (2005) 11, No. 2 (2005) 11, No. 1 (2005) 10, No. 6 (2004) 10, No. 5 (2004) 10, No. 4 (2004) 10, No. 3 (2004) 10, No. 2 (2004) 10, No. 1 (2004) 9, No. 6 (2003) 9, No. 5 (2003) 9, No. 4 (2003) 9, No. 3 (2003) 9, No. 2 (2003) 9, No. 1 (2003) 8, No. 6 (2002) 8, No. 5 (2002) 8, No. 4 (2002) 8, No. 3 (2002) 8, No. 2 (2002) 8, No. 1 (2002) 7, No. 6 (2001) 7, No. 5 (2001) 7, No. 4 (2001) 7, No. 3 (2001) 7, No. 2 (2001) 7, No. 1 (2001) 6, No. 4 (2000) 6, No. 3 (2000) 6, No. 2 (2000) 6, No. 1 (2000) 5, No. 4 (1999) 5, No. 3 (1999) 5, No. 2 (1999) 5, No. 1 (1999) 4, No. 4 (1998) 4, No. 3 (1998) 4, No. 2 (1998) 4, No. 1 (1998) 3, No. 4 (1997) 3, No. 3 (1997) 3, No. 2 (1997) 3, No. 1 (1997) 2, No. 4 (1996) 2, No. 3 (1996) 2, No. 2 (1996) 2, No. 1 (1996) 1, No. 4 (1995) 1, No. 3 (1995) 1, No. 2 (1995) 1, No. 1 (1995) 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 all cited Publications top 5 cited Publications 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 all cited Publications top 5 cited Publications all top 5 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 all top 5 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. 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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. 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Series B (English Edition) 2 Numerical Linear Algebra with Applications 2 Advances in Computational Mathematics ...and 134 more Journals all top 5 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) Citations by Year