Edit Profile (opens in new tab) Rump, Siegfried Michael Co-Author Distance Author ID: rump.siegfried-michael Published as: Rump, Siegfried M.; Rump, S. M.; Rump, Siegfried; Rump, Siegfried Michael; Rump, S. more...less Homepage: https://www.tuhh.de/ti3/rump/ External Links: MGP · ORCID · Wikidata · ResearchGate · dblp Documents Indexed: 142 Publications since 1979, including 1 Book and 1 Additional arXiv Preprint 6 Contributions as Editor · 1 Further Contribution Co-Authors: 48 Co-Authors with 61 Joint Publications 1,582 Co-Co-Authors all top 5 Co-Authors 87 single-authored 13 Ogita, Takeshi 12 Oishi, Shin’ichi 8 Bünger, Florian 7 Lange, Marko 6 Kaucher, Edgar W. 5 Kulisch, Ulrich W. 5 Ozaki, Katsuhisa 4 Jansson, Christian 4 Jeannerod, Claude-Pierre 4 Ullrich, Christian P. 3 Miranker, Willard Lee 3 Nakao, Mitsuhiro T. 2 Alefeld, Götz E. 2 Bleher, J. Hartmut 2 Bohlender, Gerd 2 Grüner, Kurt 2 Klatte, Rudi 2 Krämer, Walter 2 Kreinovich, Vladik Yakovlevich 2 Metzger, Michael 2 Radons, Manuel 2 Rohn, Jiri 2 Walter, Wolfgang 2 Wolff von Gudenberg, Jürgen 2 Yamamoto, Tetsuro 1 Batra, Prashant 1 Boldo, Sylvie 1 Buchberger, Bruno 1 Feilmeier, Manfred 1 Friedland, Shmuel 1 Graillat, Stef 1 Hershkowitz, Daniel 1 Kearfott, Baker 1 Kotsireas, Ilias S. 1 Kratz, Matthias 1 Kutzler, Bernhard 1 Lehmann, Lutz 1 Lindemann, Rudolf 1 Mackens, Wolfgang 1 Mascagni, Michael V. 1 Melquiond, Guillaume 1 Minamihata, Atsushi 1 Miyajima, Shinya 1 Neumaier, Arnold 1 Sekigawa, Hiroshi 1 Sharyĭ, Sergeĭ Petrovich 1 Strohm, Christian 1 Tanabe, Kunio 1 Van Hentenryck, Pascal 1 Yap, Chee-Keng 1 Zemke, Jens-Peter Max 1 Zimmermann, Paul all top 5 Serials 16 Linear Algebra and its Applications 15 BIT 13 Journal of Computational and Applied Mathematics 9 SIAM Journal on Matrix Analysis and Applications 8 Computing 5 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 5 Mathematics of Computation 4 Japan Journal of Industrial and Applied Mathematics 4 Numerical Algorithms 4 SIAM Journal on Scientific Computing 4 Reliable Computing 3 Elektronische Rechenanlagen 3 ELA. The Electronic Journal of Linear Algebra 2 Linear and Multilinear Algebra 2 ACM Transactions on Mathematical Software 2 ETNA. Electronic Transactions on Numerical Analysis 1 IMA Journal of Numerical Analysis 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 IEEE Transactions on Automatic Control 1 Integral Equations and Operator Theory 1 Journal of Geometry 1 Numerische Mathematik 1 Wissenschaftliche Zeitschrift 1 Applied Numerical Mathematics 1 SIAM Review 1 ZOR. Zeitschrift für Operations Research 1 Interval Computations 1 Optimization Methods & Software 1 Vychislitel’nye Tekhnologii 1 Acta Numerica 1 Lecture Notes in Computer Science 1 Mathematische Methoden in der Technik 1 Optimization Letters all top 5 Fields 126 Numerical analysis (65-XX) 43 Linear and multilinear algebra; matrix theory (15-XX) 15 Computer science (68-XX) 7 General and overarching topics; collections (00-XX) 6 Operations research, mathematical programming (90-XX) 5 Operator theory (47-XX) 3 Number theory (11-XX) 3 Field theory and polynomials (12-XX) 3 Geometry (51-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 109 Publications have been cited 1,571 times in 873 Documents Cited by ▼ Year ▼ INTLAB – INTerval LABoratory. Zbl 0949.65046 Rump, Siegfried M. 328 1999 Verification methods: rigorous results using floating-point arithmetic. Zbl 1323.65046 Rump, Siegfried M. 143 2010 Accurate sum and dot product. Zbl 1084.65041 Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 92 2005 Verification methods for dense and sparse systems of equations. Zbl 0813.65072 Rump, S. M. 65 1994 Accurate floating-point summation. I: Faithful rounding. Zbl 1185.65082 Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi 60 2008 Standardized notation in interval analysis. Zbl 1196.65088 Kearfott, R. B.; Nakao, M. T.; Neumaier, A.; Rump, S. M.; Shary, S. P.; van Hentenryck, P. 44 2010 Kleine Fehlerschranken bei Matrixproblemen. Zbl 0437.65036 Rump, Siegfried M. 31 1980 Fast and parallel interval arithmetic. Zbl 0942.65048 Rump, Siegfried M. 30 1999 Accurate floating-point summation. II: Sign, \(K\)-fold faithful and rounding to nearest. Zbl 1190.65074 Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi 29 2008 Computational error bounds for multiple or nearly multiple eigenvalues. Zbl 0986.65031 Rump, Siegfried M. 28 2001 Structured perturbations. I: Normwise distances. Zbl 1061.15004 Rump, Siegfried M. 28 2003 Eigenvalues, pseudospectrum and structured perturbations. Zbl 1093.15020 Rump, Siegfried M. 26 2006 Improved error bounds for inner products in floating-point arithmetic. Zbl 1279.65052 Jeannerod, Claude-Pierre; Rump, Siegfried M. 23 2013 Verification of positive definiteness. Zbl 1101.65039 Rump, S. M. 22 2006 Theorems of Perron-Frobenius type for matrices without sign restrictions. Zbl 0901.15002 Rump, S. M. 22 1997 Inversion of extremely ill-conditioned matrices in floating-point. Zbl 1185.65050 Rump, Siegfried M. 21 2009 Fast verification of solutions of matrix equations. Zbl 0999.65015 Oishi, Shin’Ichi; Rump, Siegfried M. 21 2002 Structured perturbations. II: Componentwise distances. Zbl 1061.15005 Rump, Siegfried M. 21 2003 Ten methods to bound multiple roots of polynomials. Zbl 1030.65046 Rump, Siegfried M. 21 2003 Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse. Zbl 1226.65028 Rump, Siegfried M. 20 2011 On the solution of interval linear systems. Zbl 0753.65030 Rump, S. M. 19 1992 Verified error bounds for multiple roots of systems of nonlinear equations. Zbl 1201.65081 Rump, Siegfried M.; Graillat, Stef 18 2010 Solving algebraic problems with high accuracy. Zbl 0597.65018 Rump, Siegfried M. 16 1983 Solving nonlinear systems with least significant bit accuracy. Zbl 0485.65036 Rump, S. M. 15 1982 Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications. Zbl 1244.65062 Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shin’ichi; Rump, Siegfried M. 15 2012 A note on epsilon-inflation. Zbl 0920.65031 Rump, Siegfried M. 15 1998 Rigorous sensitivity analysis for systems of linear and nonlinear equations. Zbl 0701.65039 Rump, Siegfried M. 15 1990 Ill-conditioned matrices are componentwise near to singularity. Zbl 0923.15003 Rump, Siegfried M. 14 1999 Polynomial minimum root separation. Zbl 0405.12018 Rump, Siegfried M. 14 1979 Improved backward error bounds for LU and Cholesky factorizations. Zbl 1309.65031 Rump, Siegfried M.; Jeannerod, Claude-Pierre 14 2014 Perron-Frobenius theory for complex matrices. Zbl 1019.15012 Rump, Siegfried M. 14 2003 Error estimation of floating-point summation and dot product. Zbl 1243.65047 Rump, Siegfried M. 13 2012 Rigorous solution of linear programming problems with uncertain data. Zbl 0735.90043 Jansson, C.; Rump, S. M. 13 1991 Ultimately fast accurate summation. Zbl 1202.65033 Rump, Siegfried M. 13 2009 Self-validating methods. Zbl 0978.65037 Rump, Siegfried M. 12 2001 Expansion and estimation of the range of bonlinear functions. Zbl 0853.65049 Rump, S. M. 12 1996 Bounds for the componentwise distance to the nearest singular matrix. Zbl 0870.65038 Rump, S. M. 12 1997 Guaranteed inclusions for the complex generalized eigenproblem. Zbl 0676.65028 Rump, S. M. 11 1989 On relative errors of floating-point operations: optimal bounds and applications. Zbl 1380.65082 Jeannerod, Claude-Pierre; Rump, Siegfried M. 11 2018 Convergence of Rump’s method for inverting arbitrarily ill-conditioned matrices. Zbl 1120.65040 Oishi, Shin’ichi; Tanabe, Kunio; Ogita, Takeshi; Rump, Siegfried M. 10 2007 On eigenvector bounds. Zbl 1042.65029 Rump, Siegfried M.; Zemke, Jens-Peter M. 10 2003 New results on verified inclusions. Zbl 0609.65033 Rump, Siegfried M. 9 1986 Verified bounds for least squares problems and underdetermined linear systems. Zbl 1255.65082 Rump, Siegfried M. 8 2012 Almost sharp bounds for the componentwise distance to the nearest singular matrix. Zbl 0877.15030 Rump, S. M. 8 1997 Validated solution of large linear systems. Zbl 0837.65013 Rump, S. M. 8 1993 FORTRAN-SC. A study of a FORTRAN extension for engineering/scientific computation with access to ACRITH. Zbl 0624.68032 Bleher, J. H.; Rump, S. M.; Kulisch, U.; Metzger, M.; Ullrich, Ch.; Walter, W. 8 1987 Accurate solution of dense linear systems. II: Algorithms using directed rounding. Zbl 1260.65034 Rump, Siegfried M. 8 2013 Super-fast validated solution of linear systems. Zbl 1108.65020 Rump, Siegfried M.; Ogita, Takeshi 7 2007 E-methods for fixed point equations f(x)=x. Zbl 0474.65039 Kaucher, E.; Rump, S. M. 7 1982 Computing predecessor and successor in rounding to nearest. Zbl 1196.65089 Rump, Siegfried M.; Zimmermann, Paul; Boldo, Sylvie; Melquiond, Guillaume 7 2009 Sharp estimates for perturbation errors in summations. Zbl 1453.65097 Lange, Marko; Rump, Siegfried M. 7 2019 A class of arbitrarily ill conditioned floating-point matrices. Zbl 0738.65042 Rump, Siegfried M. 6 1991 On \(P\)-matrices. Zbl 1044.15013 Rump, Siegfried M. 6 2003 Error estimates for the summation of real numbers with application to floating-point summation. Zbl 1380.65083 Lange, Marko; Rump, Siegfried M. 6 2017 Accurate solution of dense linear systems I: Algorithms in rounding to nearest. Zbl 1255.65084 Rump, Siegfried M. 6 2013 Small bounds for the solution of systems of linear equations. Zbl 0419.65023 Rump, S. M.; Kaucher, E. 5 1980 Fast interval matrix multiplication. Zbl 1264.65065 Rump, Siegfried M. 4 2012 Fast algorithms for floating-point interval matrix multiplication. Zbl 1248.65044 Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 4 2012 A method of obtaining verified solutions for linear systems suited for Java. Zbl 1108.65019 Ozaki, K.; Ogita, T.; Miyajima, S.; Oishi, S.; Rump, S. M. 4 2007 Ill-conditionedness need not be componentwise near to ill-posedness for least squares problems. Zbl 0970.65039 Rump, Siegfried M. 4 1999 Faithfully rounded floating-point computations. Zbl 1484.65350 Lange, Marko; Rump, Siegfried M. 4 2020 The ratio between the Toeplitz and the unstructured condition number. Zbl 1203.15004 Rump, Siegfried M.; Sekigawa, Hiroshi 4 2010 Algorithms for verified inclusions: Theory and practice. Zbl 0665.65046 Rump, Siegfried M. 3 1988 The sign-real spectral radius and cycle products. Zbl 0942.15005 Rump, Siegfried M. 3 1998 Iterative refinement for ill-conditioned linear systems. Zbl 1188.65053 Oishi, Shin’ichi; Ogita, Takeshi; Rump, Siegfried M. 3 2009 Rigorous and portable standard functions. Zbl 0994.65017 Rump, Siegfried M. 3 2001 Inclusion of zeros of nowhere differentiable \(n\)-dimensional functions. Zbl 0883.65041 Rump, Siegfried M. 3 1997 Improved componentwise verified error bounds for least squares problems and underdetermined linear systems. Zbl 1293.65062 Rump, Siegfried M. 3 2014 Improved error bounds for floating-point products and Horner’s scheme. Zbl 1342.65122 Rump, Siegfried M.; Bünger, Florian; Jeannerod, Claude-Pierre 3 2016 Variational characterizations of the sign-real and the sign-complex spectral radius. Zbl 1046.15025 Rump, Siegfried M. 3 2002 IEEE754 precision-\(k\) base-\(\beta\) arithmetic inherited by precision-\(m\) base-\(\beta\) arithmetic for \(k<m\). Zbl 1396.65177 Rump, Siegfried M. 3 2017 Bounds for the determinant by Gershgorin circles. Zbl 1405.15011 Rump, Siegfried M. 3 2019 Algebraic computation, numerical computation and verified inclusions. Zbl 0663.65043 Rump, Siegfried M. 2 1988 Solution of linear and nonlinear algebraic problems with sharp, guaranteed bounds. Zbl 0548.65037 Rump, S. M. 2 1984 Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems. Zbl 0862.65033 Rump, S. M. 2 1996 Conservatism of the circle criterion – solution of a problem posed by A. Megretski: “How conservative is the circle criterion”. Zbl 1019.93046 Rump, Siegfried M. 2 2001 Optimal scaling for \(p\)-norms and componentwise distance to singularity. Zbl 1021.65023 Rump, Siegfried M. 2 2003 Floating-point arithmetic on the test bench. How are verified numerical solutions calculated? (Gleitkommaarithmetik auf dem Prüfstand. Wie werden verifiziert(e) numerische Lösungen berechnet?) Zbl 1372.65140 Rump, Siegfried Michael 2 2016 Yet more elementary proofs that the determinant of a symplectic matrix is 1. Zbl 1352.15040 Bünger, F.; Rump, S. M. 2 2017 Simple floating-point filters for the two-dimensional orientation problem. Zbl 1347.65050 Ozaki, Katsuhisa; Bünger, Florian; Ogita, Takeshi; Oishi, Shin’ichi; Rump, Siegfried M. 2 2016 The componentwise structured and unstructured backward errors can be arbitrarily far apart. Zbl 1328.65104 Rump, Siegfried M. 2 2015 On recurrences converging to the wrong limit in finite precision and some new examples. Zbl 1448.65041 Rump, Siegfried M. 2 2020 Interval arithmetic over finitely many endpoints. Zbl 1264.65072 Rump, Siegfried M. 2 2012 Estimates of the determinant of a perturbed identity matrix. Zbl 1403.15003 Rump, Siegfried M. 2 2018 The determinant of a complex matrix and Gershgorin circles. Zbl 1430.15006 Bünger, Florian; Rump, Siegfried M. 2 2019 Solution of linear systems with verified accuracy. Zbl 0643.34014 Rump, Siegfried M. 1 1987 FORTRAN-SC: A study of a FORTRAN extension for engineering/scientific computation with access to ACRITH. Zbl 0662.68010 Bleher, J. H.; Rump, S. M.; Kulisch, U.; Metzger, M.; Ullrich, Ch.; Walter, W. 1 1988 Least significant bit evaluation of arithmetic expressions in single- precision. Zbl 0494.65020 Rump, S. M.; Boehm, H. 1 1983 Arithmetic specification in FORTRAN 8X. Zbl 0553.68022 Bohlender, Gerd; Böhm, H.; Grüner, K.; Kaucher, E.; Klatte, R.; Krämer, W.; Kulisch, U.; Miranker, W. L.; Rump, S. M.; Ullrich, Christian; Wolff von Gudenberg, Jürgen 1 1984 Inclusion of the solution for large linear systems with \(M\)-matrix. Zbl 0829.65031 Rump, Siegfried M. 1 1992 Verified solution of large systems and global optimization problems. Zbl 0866.65035 Rump, Siegfried M. 1 1995 Adaptive and efficient algorithm for 2D orientation problem. Zbl 1185.65037 Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 1 2009 Symbolic algebraic methods and verification methods. Zbl 0963.00018 1 2001 Verified solution of large linear and nonlinear systems. Zbl 0943.65039 Rump, Siegfried M. 1 1999 Towards optimal use of multi-precision arithmetic: a remark. Zbl 1098.65046 Kreinovich, Vladik; Rump, Siegfried 1 2006 Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004). Selected papers based on the presentations at the 11th GAMM-IMACS international symposium, Fukuoka, Japan, October 4–8, 2004. Zbl 1127.68306 1 2007 Computer demonstration packages for standard problems of numerical mathematics. Zbl 0597.65017 Rump, Siegfried M. 1 1983 Algorithms with result verification. – Some remarks on new developments. (Algorithmen mit Ergebnisverifikation. – Einige Bemerkungen zu neueren Entwicklungen.) Zbl 0812.65037 Jansson, Christian; Rump, Siegfried M. 1 1994 Mathematical aspects of computer and information sciences. 6th international conference, MACIS 2015, Berlin, Germany, November 11–13, 2015. Revised selected papers. Zbl 1334.68018 1 2016 On the definition of unit roundoff. Zbl 1342.65123 Rump, Siegfried M.; Lange, Marko 1 2016 Convergence results for some piecewise linear solvers. Zbl 1493.90207 Radons, Manuel; Rump, Siegfried M. 1 2022 Verified error bounds for all eigenvalues and eigenvectors of a matrix. Zbl 1508.65034 Rump, Siegfried M. 1 2022 Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin’s \(\sin (\theta)\) theorem. Zbl 1470.65088 Lange, Marko; Rump, Siegfried M. 1 2021 Faithfully rounded floating-point computations. Zbl 1484.65350 Lange, Marko; Rump, Siegfried M. 4 2020 On recurrences converging to the wrong limit in finite precision and some new examples. Zbl 1448.65041 Rump, Siegfried M. 2 2020 Addendum to: “On recurrences converging to the wrong limit in finite precision and some new examples”. Zbl 1456.65031 Rump, Siegfried M. 1 2020 Modified error bounds for approximate solutions of dense linear systems. Zbl 1433.65041 Minamihata, Atsushi; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 1 2020 Verified bounds for the determinant of real or complex point or interval matrices. Zbl 1437.65020 Rump, Siegfried M. 1 2020 Sharp estimates for perturbation errors in summations. Zbl 1453.65097 Lange, Marko; Rump, Siegfried M. 7 2019 Bounds for the determinant by Gershgorin circles. Zbl 1405.15011 Rump, Siegfried M. 3 2019 The determinant of a complex matrix and Gershgorin circles. Zbl 1430.15006 Bünger, Florian; Rump, Siegfried M. 2 2019 Lower bounds for the smallest singular value of certain Toeplitz-like triangular matrices with linearly increasing diagonal entries. Zbl 1423.15030 Bünger, Florian; Rump, Siegfried M. 1 2019 Addendum to: “Estimates of the determinant of a perturbed identity matrix”. Zbl 1410.15017 Rump, Siegfried M.; Batra, Prashant 1 2019 On relative errors of floating-point operations: optimal bounds and applications. Zbl 1380.65082 Jeannerod, Claude-Pierre; Rump, Siegfried M. 11 2018 Estimates of the determinant of a perturbed identity matrix. Zbl 1403.15003 Rump, Siegfried M. 2 2018 Mathematically rigorous global optimization in floating-point arithmetic. Zbl 1398.65093 Rump, Siegfried M. 1 2018 Error estimates for the summation of real numbers with application to floating-point summation. Zbl 1380.65083 Lange, Marko; Rump, Siegfried M. 6 2017 IEEE754 precision-\(k\) base-\(\beta\) arithmetic inherited by precision-\(m\) base-\(\beta\) arithmetic for \(k<m\). Zbl 1396.65177 Rump, Siegfried M. 3 2017 Yet more elementary proofs that the determinant of a symplectic matrix is 1. Zbl 1352.15040 Bünger, F.; Rump, S. M. 2 2017 Improved error bounds for floating-point products and Horner’s scheme. Zbl 1342.65122 Rump, Siegfried M.; Bünger, Florian; Jeannerod, Claude-Pierre 3 2016 Floating-point arithmetic on the test bench. How are verified numerical solutions calculated? (Gleitkommaarithmetik auf dem Prüfstand. Wie werden verifiziert(e) numerische Lösungen berechnet?) Zbl 1372.65140 Rump, Siegfried Michael 2 2016 Simple floating-point filters for the two-dimensional orientation problem. Zbl 1347.65050 Ozaki, Katsuhisa; Bünger, Florian; Ogita, Takeshi; Oishi, Shin’ichi; Rump, Siegfried M. 2 2016 Mathematical aspects of computer and information sciences. 6th international conference, MACIS 2015, Berlin, Germany, November 11–13, 2015. Revised selected papers. Zbl 1334.68018 1 2016 On the definition of unit roundoff. Zbl 1342.65123 Rump, Siegfried M.; Lange, Marko 1 2016 The componentwise structured and unstructured backward errors can be arbitrarily far apart. Zbl 1328.65104 Rump, Siegfried M. 2 2015 Improved backward error bounds for LU and Cholesky factorizations. Zbl 1309.65031 Rump, Siegfried M.; Jeannerod, Claude-Pierre 14 2014 Improved componentwise verified error bounds for least squares problems and underdetermined linear systems. Zbl 1293.65062 Rump, Siegfried M. 3 2014 Improved error bounds for inner products in floating-point arithmetic. Zbl 1279.65052 Jeannerod, Claude-Pierre; Rump, Siegfried M. 23 2013 Accurate solution of dense linear systems. II: Algorithms using directed rounding. Zbl 1260.65034 Rump, Siegfried M. 8 2013 Accurate solution of dense linear systems I: Algorithms in rounding to nearest. Zbl 1255.65084 Rump, Siegfried M. 6 2013 Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications. Zbl 1244.65062 Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shin’ichi; Rump, Siegfried M. 15 2012 Error estimation of floating-point summation and dot product. Zbl 1243.65047 Rump, Siegfried M. 13 2012 Verified bounds for least squares problems and underdetermined linear systems. Zbl 1255.65082 Rump, Siegfried M. 8 2012 Fast interval matrix multiplication. Zbl 1264.65065 Rump, Siegfried M. 4 2012 Fast algorithms for floating-point interval matrix multiplication. Zbl 1248.65044 Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 4 2012 Interval arithmetic over finitely many endpoints. Zbl 1264.65072 Rump, Siegfried M. 2 2012 Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse. Zbl 1226.65028 Rump, Siegfried M. 20 2011 Verification methods: rigorous results using floating-point arithmetic. Zbl 1323.65046 Rump, Siegfried M. 143 2010 Standardized notation in interval analysis. Zbl 1196.65088 Kearfott, R. B.; Nakao, M. T.; Neumaier, A.; Rump, S. M.; Shary, S. P.; van Hentenryck, P. 44 2010 Verified error bounds for multiple roots of systems of nonlinear equations. Zbl 1201.65081 Rump, Siegfried M.; Graillat, Stef 18 2010 The ratio between the Toeplitz and the unstructured condition number. Zbl 1203.15004 Rump, Siegfried M.; Sekigawa, Hiroshi 4 2010 Inversion of extremely ill-conditioned matrices in floating-point. Zbl 1185.65050 Rump, Siegfried M. 21 2009 Ultimately fast accurate summation. Zbl 1202.65033 Rump, Siegfried M. 13 2009 Computing predecessor and successor in rounding to nearest. Zbl 1196.65089 Rump, Siegfried M.; Zimmermann, Paul; Boldo, Sylvie; Melquiond, Guillaume 7 2009 Iterative refinement for ill-conditioned linear systems. Zbl 1188.65053 Oishi, Shin’ichi; Ogita, Takeshi; Rump, Siegfried M. 3 2009 Adaptive and efficient algorithm for 2D orientation problem. Zbl 1185.65037 Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 1 2009 Accurate floating-point summation. I: Faithful rounding. Zbl 1185.65082 Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi 60 2008 Accurate floating-point summation. II: Sign, \(K\)-fold faithful and rounding to nearest. Zbl 1190.65074 Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi 29 2008 Convergence of Rump’s method for inverting arbitrarily ill-conditioned matrices. Zbl 1120.65040 Oishi, Shin’ichi; Tanabe, Kunio; Ogita, Takeshi; Rump, Siegfried M. 10 2007 Super-fast validated solution of linear systems. Zbl 1108.65020 Rump, Siegfried M.; Ogita, Takeshi 7 2007 A method of obtaining verified solutions for linear systems suited for Java. Zbl 1108.65019 Ozaki, K.; Ogita, T.; Miyajima, S.; Oishi, S.; Rump, S. M. 4 2007 Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004). Selected papers based on the presentations at the 11th GAMM-IMACS international symposium, Fukuoka, Japan, October 4–8, 2004. Zbl 1127.68306 1 2007 Eigenvalues, pseudospectrum and structured perturbations. Zbl 1093.15020 Rump, Siegfried M. 26 2006 Verification of positive definiteness. Zbl 1101.65039 Rump, S. M. 22 2006 Towards optimal use of multi-precision arithmetic: a remark. Zbl 1098.65046 Kreinovich, Vladik; Rump, Siegfried 1 2006 Accurate sum and dot product. Zbl 1084.65041 Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 92 2005 Structured perturbations. I: Normwise distances. Zbl 1061.15004 Rump, Siegfried M. 28 2003 Structured perturbations. II: Componentwise distances. Zbl 1061.15005 Rump, Siegfried M. 21 2003 Ten methods to bound multiple roots of polynomials. Zbl 1030.65046 Rump, Siegfried M. 21 2003 Perron-Frobenius theory for complex matrices. Zbl 1019.15012 Rump, Siegfried M. 14 2003 On eigenvector bounds. Zbl 1042.65029 Rump, Siegfried M.; Zemke, Jens-Peter M. 10 2003 On \(P\)-matrices. Zbl 1044.15013 Rump, Siegfried M. 6 2003 Optimal scaling for \(p\)-norms and componentwise distance to singularity. Zbl 1021.65023 Rump, Siegfried M. 2 2003 Fast verification of solutions of matrix equations. Zbl 0999.65015 Oishi, Shin’Ichi; Rump, Siegfried M. 21 2002 Variational characterizations of the sign-real and the sign-complex spectral radius. Zbl 1046.15025 Rump, Siegfried M. 3 2002 Computational error bounds for multiple or nearly multiple eigenvalues. Zbl 0986.65031 Rump, Siegfried M. 28 2001 Self-validating methods. Zbl 0978.65037 Rump, Siegfried M. 12 2001 Rigorous and portable standard functions. Zbl 0994.65017 Rump, Siegfried M. 3 2001 Conservatism of the circle criterion – solution of a problem posed by A. Megretski: “How conservative is the circle criterion”. Zbl 1019.93046 Rump, Siegfried M. 2 2001 Symbolic algebraic methods and verification methods. Zbl 0963.00018 1 2001 INTLAB – INTerval LABoratory. Zbl 0949.65046 Rump, Siegfried M. 328 1999 Fast and parallel interval arithmetic. Zbl 0942.65048 Rump, Siegfried M. 30 1999 Ill-conditioned matrices are componentwise near to singularity. Zbl 0923.15003 Rump, Siegfried M. 14 1999 Ill-conditionedness need not be componentwise near to ill-posedness for least squares problems. Zbl 0970.65039 Rump, Siegfried M. 4 1999 Verified solution of large linear and nonlinear systems. Zbl 0943.65039 Rump, Siegfried M. 1 1999 A note on epsilon-inflation. Zbl 0920.65031 Rump, Siegfried M. 15 1998 The sign-real spectral radius and cycle products. Zbl 0942.15005 Rump, Siegfried M. 3 1998 Theorems of Perron-Frobenius type for matrices without sign restrictions. Zbl 0901.15002 Rump, S. M. 22 1997 Bounds for the componentwise distance to the nearest singular matrix. Zbl 0870.65038 Rump, S. M. 12 1997 Almost sharp bounds for the componentwise distance to the nearest singular matrix. Zbl 0877.15030 Rump, S. M. 8 1997 Inclusion of zeros of nowhere differentiable \(n\)-dimensional functions. Zbl 0883.65041 Rump, Siegfried M. 3 1997 Expansion and estimation of the range of bonlinear functions. Zbl 0853.65049 Rump, S. M. 12 1996 Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems. Zbl 0862.65033 Rump, S. M. 2 1996 Verified solution of large systems and global optimization problems. Zbl 0866.65035 Rump, Siegfried M. 1 1995 Verification methods for dense and sparse systems of equations. Zbl 0813.65072 Rump, S. M. 65 1994 Algorithms with result verification. – Some remarks on new developments. (Algorithmen mit Ergebnisverifikation. – Einige Bemerkungen zu neueren Entwicklungen.) Zbl 0812.65037 Jansson, Christian; Rump, Siegfried M. 1 1994 Validated solution of large linear systems. Zbl 0837.65013 Rump, S. M. 8 1993 On the solution of interval linear systems. Zbl 0753.65030 Rump, S. M. 19 1992 Inclusion of the solution for large linear systems with \(M\)-matrix. Zbl 0829.65031 Rump, Siegfried M. 1 1992 Rigorous solution of linear programming problems with uncertain data. Zbl 0735.90043 Jansson, C.; Rump, S. M. 13 1991 A class of arbitrarily ill conditioned floating-point matrices. Zbl 0738.65042 Rump, Siegfried M. 6 1991 Rigorous sensitivity analysis for systems of linear and nonlinear equations. Zbl 0701.65039 Rump, Siegfried M. 15 1990 Guaranteed inclusions for the complex generalized eigenproblem. Zbl 0676.65028 Rump, S. M. 11 1989 Algorithms for verified inclusions: Theory and practice. Zbl 0665.65046 Rump, Siegfried M. 3 1988 Algebraic computation, numerical computation and verified inclusions. Zbl 0663.65043 Rump, Siegfried M. 2 1988 FORTRAN-SC: A study of a FORTRAN extension for engineering/scientific computation with access to ACRITH. Zbl 0662.68010 Bleher, J. H.; Rump, S. M.; Kulisch, U.; Metzger, M.; Ullrich, Ch.; Walter, W. 1 1988 FORTRAN-SC. A study of a FORTRAN extension for engineering/scientific computation with access to ACRITH. Zbl 0624.68032 Bleher, J. H.; Rump, S. M.; Kulisch, U.; Metzger, M.; Ullrich, Ch.; Walter, W. 8 1987 Solution of linear systems with verified accuracy. Zbl 0643.34014 Rump, Siegfried M. 1 1987 New results on verified inclusions. Zbl 0609.65033 Rump, Siegfried M. 9 1986 Solution of linear and nonlinear algebraic problems with sharp, guaranteed bounds. Zbl 0548.65037 Rump, S. M. 2 1984 ...and 9 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,015 Authors 58 Rump, Siegfried Michael 35 Nakao, Mitsuhiro T. 33 Lessard, Jean-Philippe 33 Oishi, Shin’ichi 32 Miyajima, Shinya 27 Ogita, Takeshi 25 Hladík, Milan 23 Mireles-James, Jason D. 22 Watanabe, Yoshitaka 15 Graillat, Stef 15 Ozaki, Katsuhisa 15 Wei, Yimin 14 van den Berg, Jan Bouwe 12 Kinoshita, Takehiko 11 Jiang, Hao 10 Sharyĭ, Sergeĭ Petrovich 10 Takayasu, Akitoshi 9 Diao, Huaian 9 Neumaier, Arnold 9 Plum, Michael 9 Tanaka, Kazuaki 8 Breden, Maxime 8 Bünger, Florian 8 Castelli, Roberto 8 Dehghani-Madiseh, Marzieh 8 Hashemi, Behnam 8 Liu, Xuefeng 8 Minamoto, Teruya 8 Muller, Jean-Michel 8 Popova, Evgeniya D. 8 Yamamoto, Nobito 7 Cheng, Lizhi 7 Domes, Ferenc 7 Goldsztejn, Alexandre 7 Higham, Nicholas J. 7 Jeannerod, Claude-Pierre 7 Kimura, Takuma 7 Mayer, Günter 7 Melquiond, Guillaume 7 Nagatou, Kaori 7 Petković, Miodrag S. 7 Skalna, Iwona 7 Wanner, Thomas 6 Barrio, Roberto 6 Capinski, Maciej J. 6 Eichfelder, Gabriele 6 Frommer, Andreas 6 Jaquette, Jonathan 6 Kearfott, Baker 6 Kolev, Lubomir V. 6 Li, Zhe 6 Mary, Theo A. 6 Mizuguchi, Makoto 6 Rohn, Jiri 6 Ryoo, Cheon Seoung 6 Schichl, Hermann 5 Alefeld, Götz E. 5 Boldo, Sylvie 5 Church, Kevin E. M. 5 Dehghan Takht Fooladi, Mehdi 5 Du, Peibing 5 Krämer, Walter 5 Kressner, Daniel 5 Lange, Marko 5 Li, Hanyu 5 Noschese, Silvia 5 Pan, Victor Yakovlevich 5 Pham Huu Anh Ngoc 5 Radons, Manuel 5 Roux, Pierre 5 Sekine, Kouta 5 Zhi, Lihong 4 Auer, Ekaterina 4 Chen, Xiaojun 4 Csendes, Tibor 4 Gameiro, Marcio F. 4 Griewank, Andreas 4 Hashimoto, Kouji 4 Jansson, Christian 4 Kepley, Shane 4 Kubica, Bartłomiej Jacek 4 Mullen, Robert L. 4 Okamoto, Hisashi 4 Rauh, Andreas 4 Sander, Evelyn 3 Adhikari, Bibhas 3 Aishima, Kensuke 3 Cai, Shuting 3 Černý, Michal 3 Cheng, Jinsan 3 Cucker, Felipe 3 Dobner, Hans-Jürgen 3 Eftekhari, Tahereh 3 Fernandes, Luiz Gustavo 3 Franek, Peter 3 García-Azpeitia, Carlos 3 Garloff, Jürgen 3 Hartman, David 3 Jermann, Christophe 3 Jézéquel, Fabienne ...and 915 more Authors all top 5 Cited in 210 Serials 92 Journal of Computational and Applied Mathematics 62 Linear Algebra and its Applications 37 Computing 36 Japan Journal of Industrial and Applied Mathematics 34 Applied Mathematics and Computation 27 Numerical Algorithms 22 BIT 21 Journal of Global Optimization 17 Journal of Differential Equations 17 Reliable Computing 15 Computers & Mathematics with Applications 12 Numerische Mathematik 11 SIAM Journal on Matrix Analysis and Applications 11 SIAM Journal on Applied Dynamical Systems 10 Mathematics of Computation 10 Theoretical Computer Science 10 Journal of Symbolic Computation 9 Applied Numerical Mathematics 9 SIAM Journal on Scientific Computing 9 Numerical Linear Algebra with Applications 8 Communications in Nonlinear Science and Numerical Simulation 7 Automatica 7 Calcolo 7 Journal of Automated Reasoning 7 Journal of Dynamics and Differential Equations 7 ELA. The Electronic Journal of Linear Algebra 6 Journal of Mathematical Analysis and Applications 6 ACM Transactions on Mathematical Software 6 Journal of Computational Dynamics 5 Journal of Computational Physics 5 Mathematical Programming. Series A. Series B 5 Computational and Applied Mathematics 5 Optimization Methods & Software 5 Mathematics in Computer Science 4 Linear and Multilinear Algebra 4 Nonlinearity 4 SIAM Journal on Numerical Analysis 4 Physica D 4 International Journal of Computer Mathematics 4 Indagationes Mathematicae. New Series 4 ETNA. Electronic Transactions on Numerical Analysis 4 Advances in Computational Mathematics 4 Soft Computing 4 Foundations of Computational Mathematics 4 Optimization Letters 4 Journal of Mathematical Modeling 3 Mathematics and Computers in Simulation 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Numerical Functional Analysis and Optimization 3 Computers & Operations Research 3 Applications of Mathematics 3 Celestial Mechanics and Dynamical Astronomy 3 Applicable Algebra in Engineering, Communication and Computing 3 International Journal of Robust and Nonlinear Control 3 Journal of Nonlinear Science 3 Formal Methods in System Design 3 Engineering Analysis with Boundary Elements 3 Constraints 3 Chaos 3 Methodology and Computing in Applied Probability 3 Journal of Systems Science and Complexity 2 Artificial Intelligence 2 Archive for Rational Mechanics and Analysis 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of the Franklin Institute 2 Information Sciences 2 International Journal for Numerical Methods in Engineering 2 Systems & Control Letters 2 Acta Applicandae Mathematicae 2 Discrete & Computational Geometry 2 Information and Computation 2 Applied Mathematics Letters 2 Journal of Scientific Computing 2 Computational Statistics 2 Applied Mathematical Modelling 2 European Journal of Operational Research 2 SIAM Journal on Mathematical Analysis 2 SIAM Journal on Optimization 2 Discrete and Continuous Dynamical Systems 2 Mathematical Problems in Engineering 2 Journal of Inequalities and Applications 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 2 International Journal of Applied Mathematics and Computer Science 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Applied Mathematics 2 Central European Journal of Mathematics 2 JSIAM Letters 2 Computational Methods for Differential Equations 1 American Mathematical Monthly 1 Computers and Fluids 1 Computer Physics Communications 1 Communications on Pure and Applied Mathematics 1 General Relativity and Gravitation 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 Inverse Problems 1 Information Processing Letters 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Engineering Mathematics 1 Journal of Mathematical Physics ...and 110 more Serials all top 5 Cited in 52 Fields 639 Numerical analysis (65-XX) 173 Linear and multilinear algebra; matrix theory (15-XX) 106 Partial differential equations (35-XX) 104 Operations research, mathematical programming (90-XX) 91 Computer science (68-XX) 62 Ordinary differential equations (34-XX) 53 Dynamical systems and ergodic theory (37-XX) 41 Operator theory (47-XX) 38 Systems theory; control (93-XX) 22 Fluid mechanics (76-XX) 19 Mechanics of particles and systems (70-XX) 19 Mechanics of deformable solids (74-XX) 17 Functions of a complex variable (30-XX) 15 Field theory and polynomials (12-XX) 15 Real functions (26-XX) 15 Calculus of variations and optimal control; optimization (49-XX) 14 Approximations and expansions (41-XX) 14 Statistics (62-XX) 13 Probability theory and stochastic processes (60-XX) 12 Commutative algebra (13-XX) 10 Number theory (11-XX) 9 Special functions (33-XX) 8 Algebraic geometry (14-XX) 8 Information and communication theory, circuits (94-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Combinatorics (05-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Biology and other natural sciences (92-XX) 5 Mathematical logic and foundations (03-XX) 5 Difference and functional equations (39-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Integral equations (45-XX) 5 Functional analysis (46-XX) 4 Manifolds and cell complexes (57-XX) 4 Optics, electromagnetic theory (78-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Measure and integration (28-XX) 3 Convex and discrete geometry (52-XX) 3 Algebraic topology (55-XX) 2 Group theory and generalizations (20-XX) 2 Geometry (51-XX) 2 Differential geometry (53-XX) 2 Quantum theory (81-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Associative rings and algebras (16-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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