Edit Profile (opens in new tab) Ratschek, Helmut Co-Author Distance Author ID: ratschek.helmut Published as: Ratschek, H.; Ratschek, Helmut Documents Indexed: 66 Publications since 1969, including 7 Books 1 Contribution as Editor Reviewing Activity: 193 Reviews Co-Authors: 7 Co-Authors with 34 Joint Publications 110 Co-Co-Authors all top 5 Co-Authors 27 single-authored 24 Rokne, Jon G. 4 Ecker, Klaus H. 2 Sonnenschein, Christiane 2 Voller, Rudolf L. 1 Gavrilova, Marina L. 1 Harzheim, Egbert 1 Sauer, Wilfried all top 5 Serials 7 Computing 6 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 4 Reliable Computing 3 SIAM Journal on Numerical Analysis 3 CAD. Computer-Aided Design 3 Journal of Global Optimization 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Nachrichten 2 Berichte der Gesellschaft für Mathematik und Datenverarbeitung, Bonn 1 Acta Informatica 1 Computers & Mathematics with Applications 1 Journal of Mathematical Analysis and Applications 1 Applied Mathematics and Computation 1 Journal of Approximation Theory 1 Mathematical Programming 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Control and Optimization 1 Applied Mathematics Letters 1 International Journal of Computational Geometry & Applications 1 Angewandte Informatik 1 Elemente der Mathematik 1 Glasnik Matematički. Serija III 1 International Journal of Computer Mathematics 1 Mathematical Programming. Series A. Series B 1 JMMA. Journal of Mathematical Modelling and Algorithms 1 Mathematisch-Physikalische Semesterberichte, Neue Folge 1 Beiträge zur Numerischen Mathematik all top 5 Fields 54 Numerical analysis (65-XX) 12 Operations research, mathematical programming (90-XX) 7 Computer science (68-XX) 6 Approximations and expansions (41-XX) 4 General algebraic systems (08-XX) 4 Group theory and generalizations (20-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 Mathematical logic and foundations (03-XX) 2 Field theory and polynomials (12-XX) 2 Functional analysis (46-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geometry (51-XX) 2 Convex and discrete geometry (52-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 General topology (54-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 44 Publications have been cited 537 times in 373 Documents Cited by ▼ Year ▼ New computer methods for global optimization. Zbl 0648.65049 Ratschek, H.; Rokne, J. 171 1988 Computer methods for the range of functions. Zbl 0584.65019 Ratschek, H.; Rokne, J. 123 1984 Centered forms. Zbl 0456.65019 Ratschek, H. 22 1980 Inclusion functions and global optimization. Zbl 0579.90082 Ratschek, H. 20 1985 Inclusion functions and global optimization. II. Zbl 0644.90074 Moore, R. E.; Ratschek, H. 17 1988 Centered forms for functions in several variables. Zbl 0471.65025 Ratschek, H.; Schröder, G. 13 1981 Linear interval equations. Zbl 0468.65025 Ratschek, H.; Sauer, W. 11 1982 Experiments using interval analysis for solving a circuit design problem. Zbl 0793.90077 Ratschek, H.; Rokne, J. 11 1993 Interval methods. Zbl 0832.90109 Ratschek, Helmut; Rokne, Jon 11 1995 Teilbarkeitskriterien der Intervallarithmetik. Zbl 0237.65032 Ratschek, H. 11 1972 Die binären Systeme der Intervallarithmetik. (The binary systems of interval arithmetic). Zbl 0222.65003 Ratschek, H. 10 1970 Representation of semigroups as systems of compact convex sets. Zbl 0369.20042 Ratschek, H.; Schröder, G. 9 1977 What can interval analysis do for global optimization? Zbl 0752.65054 Ratschek, H.; Voller, R. L. 9 1991 Geometric computations with interval and new robust methods. Applications in computer graphics, GIS and computational geometry. Zbl 1040.65021 Ratschek, Helmut; Rokne, Jon 9 2003 Nichtnumerische Aspekte der Intervallmathematik. Zbl 0303.65039 Ratschek, H. 7 1975 Zentrische Formen. Zbl 0385.65020 Ratschek, H. 7 1978 Efficiency of a global optimization algorithm. Zbl 0636.65060 Ratschek, H.; Rokne, J. G. 7 1987 Die Subdistributivität der Intervallarithmetik. Zbl 0214.40902 Ratschek, H. 7 1971 About the centered form. Zbl 0446.65018 Ratschek, H.; Rokne, J. 6 1980 Über die Ableitung von intervallwertigen Funktionen. (On the derivative of interval-valued functions). Zbl 0221.65032 Ratschek, H.; Schröder, G. 6 1971 Über den quasilinearen Raum. Zbl 0344.15004 Ratschek, H.; Schröder, G. 5 1976 Gleichheit von Produkt und Formalprodukt bei Intervallpolynomen. Zbl 0251.65037 Ratschek, H. 5 1972 Exact computation of Delaunay and power triangulations. Zbl 0954.65013 Gavrilova, Marina; Ratschek, Helmut; Rokne, Jon G. 4 2000 Interval tools for global optimization. Zbl 0728.65060 Ratschek, H.; Rokne, J. 4 1991 Representation of interval operations by coordinates. Zbl 0435.65039 Ratschek, H. 3 1980 Exact computation of the sign of a finite sum. Zbl 0936.65005 Ratschek, Helmut; Rokne, Jon 3 1999 Global optimization over unbounded domains. Zbl 0725.90086 Ratschek, H.; Voller, R. L. 3 1990 Ergebnisse einer Untersuchung über die Struktur von Intervallpolynomen. Zbl 0237.65033 Ratschek, Helmut 3 1972 Global interval methods for local nonsmooth optimization. Zbl 0946.90085 Görges, Christiane; Ratschek, Helmut 2 1999 Über das Produkt von Intervallpolynomen. Zbl 0301.65025 Ratschek, H. 2 1974 Über einige intervallarithmetische Grundbegriffe. Zbl 0206.46103 Ratschek, H. 2 1969 Test for intersection between plane and box. Zbl 0776.65032 Ratschek, H.; Rokne, J. 2 1993 Eigenschaften der von linearen Automaten erkennbaren Worte. Zbl 0272.94027 Ecker, K.; Ratschek, H. 1 1974 Intervallarithmetik - mit Zirkel und Lineal. Zbl 0277.65022 Ratschek, H. 1 1973 Mittelwertsätze für Intervallfunktionen. Zbl 0359.65038 Ratschek, Helmut 1 1977 Die subdirekte Unzerlegbarkeit der Intervallrechnung. Zbl 0367.08003 Ratschek, H. 1 1978 Introduction to the special issue: What can one learn from box-plane intersections? Zbl 0985.65041 Ratschek, Helmut; Rokne, Jon G. 1 2000 Some recent aspects of interval algorithms for global optimization. Zbl 0653.65047 Ratschek, Helmut 1 1988 Formulas for the width of interval products. Zbl 0844.65039 Ratschek, Helmut; Rokne, Jon G. 1 1995 Optimality of the centered form. Zbl 0549.65024 Ratschek, Helmut; Rokne, Jon 1 1980 Optimal approximations in interval analysis. Zbl 0549.65025 Ratschek, Helmut 1 1980 Optimality of the centered form for polynomials. Zbl 0479.41005 Ratschek, H.; Rokne, J. 1 1981 Universal inclusion structures. Zbl 0483.08001 Ratschek, H. 1 1982 How trivial are reliable box-plane intersections? Zbl 1206.65059 Ratschek, H.; Rokne, J. G. 1 2000 Geometric computations with interval and new robust methods. Applications in computer graphics, GIS and computational geometry. Zbl 1040.65021 Ratschek, Helmut; Rokne, Jon 9 2003 Exact computation of Delaunay and power triangulations. Zbl 0954.65013 Gavrilova, Marina; Ratschek, Helmut; Rokne, Jon G. 4 2000 Introduction to the special issue: What can one learn from box-plane intersections? Zbl 0985.65041 Ratschek, Helmut; Rokne, Jon G. 1 2000 How trivial are reliable box-plane intersections? Zbl 1206.65059 Ratschek, H.; Rokne, J. G. 1 2000 Exact computation of the sign of a finite sum. Zbl 0936.65005 Ratschek, Helmut; Rokne, Jon 3 1999 Global interval methods for local nonsmooth optimization. Zbl 0946.90085 Görges, Christiane; Ratschek, Helmut 2 1999 Interval methods. Zbl 0832.90109 Ratschek, Helmut; Rokne, Jon 11 1995 Formulas for the width of interval products. Zbl 0844.65039 Ratschek, Helmut; Rokne, Jon G. 1 1995 Experiments using interval analysis for solving a circuit design problem. Zbl 0793.90077 Ratschek, H.; Rokne, J. 11 1993 Test for intersection between plane and box. Zbl 0776.65032 Ratschek, H.; Rokne, J. 2 1993 What can interval analysis do for global optimization? Zbl 0752.65054 Ratschek, H.; Voller, R. L. 9 1991 Interval tools for global optimization. Zbl 0728.65060 Ratschek, H.; Rokne, J. 4 1991 Global optimization over unbounded domains. Zbl 0725.90086 Ratschek, H.; Voller, R. L. 3 1990 New computer methods for global optimization. Zbl 0648.65049 Ratschek, H.; Rokne, J. 171 1988 Inclusion functions and global optimization. II. Zbl 0644.90074 Moore, R. E.; Ratschek, H. 17 1988 Some recent aspects of interval algorithms for global optimization. Zbl 0653.65047 Ratschek, Helmut 1 1988 Efficiency of a global optimization algorithm. Zbl 0636.65060 Ratschek, H.; Rokne, J. G. 7 1987 Inclusion functions and global optimization. Zbl 0579.90082 Ratschek, H. 20 1985 Computer methods for the range of functions. Zbl 0584.65019 Ratschek, H.; Rokne, J. 123 1984 Linear interval equations. Zbl 0468.65025 Ratschek, H.; Sauer, W. 11 1982 Universal inclusion structures. Zbl 0483.08001 Ratschek, H. 1 1982 Centered forms for functions in several variables. Zbl 0471.65025 Ratschek, H.; Schröder, G. 13 1981 Optimality of the centered form for polynomials. Zbl 0479.41005 Ratschek, H.; Rokne, J. 1 1981 Centered forms. Zbl 0456.65019 Ratschek, H. 22 1980 About the centered form. Zbl 0446.65018 Ratschek, H.; Rokne, J. 6 1980 Representation of interval operations by coordinates. Zbl 0435.65039 Ratschek, H. 3 1980 Optimality of the centered form. Zbl 0549.65024 Ratschek, Helmut; Rokne, Jon 1 1980 Optimal approximations in interval analysis. Zbl 0549.65025 Ratschek, Helmut 1 1980 Zentrische Formen. Zbl 0385.65020 Ratschek, H. 7 1978 Die subdirekte Unzerlegbarkeit der Intervallrechnung. Zbl 0367.08003 Ratschek, H. 1 1978 Representation of semigroups as systems of compact convex sets. Zbl 0369.20042 Ratschek, H.; Schröder, G. 9 1977 Mittelwertsätze für Intervallfunktionen. Zbl 0359.65038 Ratschek, Helmut 1 1977 Über den quasilinearen Raum. Zbl 0344.15004 Ratschek, H.; Schröder, G. 5 1976 Nichtnumerische Aspekte der Intervallmathematik. Zbl 0303.65039 Ratschek, H. 7 1975 Über das Produkt von Intervallpolynomen. Zbl 0301.65025 Ratschek, H. 2 1974 Eigenschaften der von linearen Automaten erkennbaren Worte. Zbl 0272.94027 Ecker, K.; Ratschek, H. 1 1974 Intervallarithmetik - mit Zirkel und Lineal. Zbl 0277.65022 Ratschek, H. 1 1973 Teilbarkeitskriterien der Intervallarithmetik. Zbl 0237.65032 Ratschek, H. 11 1972 Gleichheit von Produkt und Formalprodukt bei Intervallpolynomen. Zbl 0251.65037 Ratschek, H. 5 1972 Ergebnisse einer Untersuchung über die Struktur von Intervallpolynomen. Zbl 0237.65033 Ratschek, Helmut 3 1972 Die Subdistributivität der Intervallarithmetik. Zbl 0214.40902 Ratschek, H. 7 1971 Über die Ableitung von intervallwertigen Funktionen. (On the derivative of interval-valued functions). Zbl 0221.65032 Ratschek, H.; Schröder, G. 6 1971 Die binären Systeme der Intervallarithmetik. (The binary systems of interval arithmetic). Zbl 0222.65003 Ratschek, H. 10 1970 Über einige intervallarithmetische Grundbegriffe. Zbl 0206.46103 Ratschek, H. 2 1969 all cited Publications top 5 cited Publications all top 5 Cited by 403 Authors 36 Rokne, Jon G. 19 Ratschek, Helmut 18 Csendes, Tibor 14 Messine, Frédéric 13 Gazdag-Tóth, Boglárka 13 Lin, Qun 11 Fernandez Hernandez, Jose 11 Hansen, Pierre 9 Nataraj, Paluri S. V. 8 Kearfott, Baker 8 Ozdamar, Linet 7 Floudas, Christodoulos Achilleus 6 Jaumard, Brigitte 6 Pelegrín, Blas 6 Pintér, János D. 5 Audet, Charles 5 Casado, Leocadio G. 5 Jaulin, Luc 5 Kreinovich, Vladik Yakovlevich 5 Markót, Mihály Csaba 5 Mitsos, Alexander 5 Pedamallu, Chandra Sekhar 5 Plastria, Frank 5 Sergeev, Yaroslav Dmitrievich 5 Wolfe, Michael A. 4 Alefeld, Götz E. 4 Barton, Paul I. 4 Grzybowski, Jerzy 4 Ninin, Jordan 4 Scholz, Daniel 4 Sharyĭ, Sergeĭ Petrovich 4 Urbański, Ryszard 3 Bánhelyi, Balázs 3 Bao, Paul G. 3 Carrizosa, Emilio 3 Galperin, Efim A. 3 Grapsa, Theodoula N. 3 Jansson, Christian 3 Markov, Svetoslav Marinovich 3 Najman, Jaromił 3 Nickel, Karl L. E. 3 Shen, Zuhe 3 Sotiropoulos, Dimitris G. 3 Visweswaran, V. 3 Walter, Eric 3 Xiong, Junjie 3 Xu, Peiliang 3 Zhang, Liansheng 2 Arounassalame, M. 2 Bahoo, Yeganeh 2 Behnke, Henning 2 Belotti, Pietro 2 Bhunia, Asoke Kumar 2 Bompadre, Agustín 2 Burr, Michael A. 2 Cao, Dexin 2 Chachuat, Benoît 2 Chen, Chin-Yun 2 Csallner, András Erik 2 Demirhan, Melek Basak 2 Dian, Jianwei 2 Dobner, Hans-Jürgen 2 Dulikravich, George Stevo 2 Durocher, Stephane 2 Dyllong, Eva 2 García, Inmaculada F. 2 Gavrilova, Marina L. 2 Ge, Renpu 2 Georg, Kurt 2 Goualard, Frédéric 2 Hansen, Eldon Robert 2 Hendrix, Eligius M. T. 2 Hladík, Milan 2 Huang, Chungyuan 2 Karmakar, Samiran 2 Keil, J. Mark 2 Kubal, Nandkishor 2 Kubica, Bartłomiej Jacek 2 Kulpa, Zenon 2 Lagouanelle, Jean-Louis 2 Le Thi, Hoai An 2 Lohner, Rudolf J. 2 Lu, Shihui 2 Lupulescu, Vasile 2 Maranas, Costas D. 2 Martin, Ralph R. 2 Mayer, Günter 2 Mehrabi, Saeed 2 Mehrpour, Sahar 2 Milanese, Mario 2 Mondal, Debajyoti 2 Neumaier, Arnold 2 Ouanes, Mohand 2 Pallaschke, Diethard 2 Paluri, Nataraj S. V. 2 Panovskiy, V. N. 2 Panteleev, Andreĭ Vladimirovich 2 Pardalos, Panos M. 2 Patil, Bhagyesh V. 2 Piazzi, Aurelio ...and 303 more Authors all top 5 Cited in 97 Serials 62 Journal of Global Optimization 51 Computing 24 Journal of Computational and Applied Mathematics 18 Reliable Computing 16 Applied Mathematics and Computation 12 Computers & Mathematics with Applications 11 Computers & Operations Research 10 Journal of Optimization Theory and Applications 9 Mathematical Programming. Series A. Series B 7 BIT 6 Fuzzy Sets and Systems 6 European Journal of Operational Research 5 Automatica 5 Annals of Operations Research 4 Computer Aided Geometric Design 4 Numerical Algorithms 4 International Journal of Computer Mathematics 4 Linear Algebra and its Applications 3 Discrete & Computational Geometry 3 Mathematical and Computer Modelling 3 International Journal of Computational Geometry & Applications 3 Applied Mathematical Modelling 2 Artificial Intelligence 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Naval Research Logistics 2 Theoretical Computer Science 2 Applied Numerical Mathematics 2 Journal of Symbolic Computation 2 Journal of Complexity 2 Abstract and Applied Analysis 2 Optimization and Engineering 2 RAIRO. Operations Research 2 Structural and Multidisciplinary Optimization 2 Optimization Letters 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal of Control 1 International Journal of Systems Science 1 Journal of the Franklin Institute 1 Journal of Mathematical Analysis and Applications 1 Mathematics of Computation 1 ACM Transactions on Mathematical Software 1 Advances in Mathematics 1 Algebra Universalis 1 Aplikace Matematiky 1 Journal of Approximation Theory 1 Journal of Combinatorial Theory. Series A 1 Journal of Differential Equations 1 Journal of Soviet Mathematics 1 Mathematics and Computers in Simulation 1 Mathematical Programming 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Opsearch 1 Proceedings of the American Mathematical Society 1 Semigroup Forum 1 Siberian Mathematical Journal 1 Journal of Information & Optimization Sciences 1 Zeitschrift für Analysis und ihre Anwendungen 1 Acta Applicandae Mathematicae 1 Optimization 1 Computational Mechanics 1 COMPEL 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 Neural Networks 1 Automation and Remote Control 1 Computational Statistics and Data Analysis 1 ZOR. Zeitschrift für Operations Research 1 International Journal of Robust and Nonlinear Control 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Computational Optimization and Applications 1 Computational Economics 1 Journal of Computer and Systems Sciences International 1 Applied Mathematics. Series B (English Edition) 1 Journal of the Egyptian Mathematical Society 1 Top 1 Annals of Mathematics and Artificial Intelligence 1 Constraints 1 ELA. The Electronic Journal of Linear Algebra 1 Mathematical Problems in Engineering 1 European Journal of Control 1 Optimization Methods & Software 1 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 1 CEJOR. Central European Journal of Operations Research 1 International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 1 Advances in Geometry 1 Journal of Systems Science and Complexity 1 OR Spectrum 1 SIAM Journal on Applied Dynamical Systems 1 4OR 1 Boletim da Sociedade Paranaense de Matemática. Terceira Série 1 Networks and Spatial Economics 1 Engineering Optimization 1 Set-Valued and Variational Analysis 1 Journal of the Operations Research Society of China 1 Nonlinear Analysis. Theory, Methods & Applications all top 5 Cited in 40 Fields 220 Numerical analysis (65-XX) 188 Operations research, mathematical programming (90-XX) 34 Computer science (68-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 18 Systems theory; control (93-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 12 Approximations and expansions (41-XX) 12 Convex and discrete geometry (52-XX) 11 Real functions (26-XX) 11 Functions of a complex variable (30-XX) 8 Ordinary differential equations (34-XX) 6 Statistics (62-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Functional analysis (46-XX) 4 Mechanics of particles and systems (70-XX) 4 Mechanics of deformable solids (74-XX) 2 Mathematical logic and foundations (03-XX) 2 General algebraic systems (08-XX) 2 Group theory and generalizations (20-XX) 2 Topological groups, Lie groups (22-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Optics, electromagnetic theory (78-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX) Citations by Year