Edit Profile (opens in new tab) Rump, Siegfried Michael Compute Distance To: Compute Author ID: rump.siegfried-michael Published as: Rump, Siegfried M.; Rump, S. M.; Rump, Siegfried; Rump, Siegfried Michael; Rump, S. more...less Documents Indexed: 137 Publications since 1979, including 1 Book 6 Contributions as Editor · 1 Further Contribution Co-Authors: 47 Co-Authors with 58 Joint Publications 1,406 Co-Co-Authors all top 5 Co-Authors 85 single-authored 13 Ogita, Takeshi 12 Oishi, Shin’ichi 7 Bünger, Florian 6 Kaucher, Edgar W. 6 Lange, Marko 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 Rohn, Jiri 2 Walter, Wolfgang 2 Wolff von Gudenberg, Jürgen 2 Yamamoto, Tetsuro 1 Batra, Prashant 1 Boldo, Sylvie 1 Buchberger, Bruno 1 Dennis, David J. C. 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 Lindemann, Rudolf 1 Mackens, Wolfgang 1 Mascagni, Michael V. 1 Melquiond, Guillaume 1 Minamihata, Atsushi 1 Miyajima, Shinya 1 Neumaier, Arnold 1 Radons, Manuel 1 Sekigawa, Hiroshi 1 Sharyĭ, Sergeĭ Petrovich 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 14 BIT 12 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 Numerical Algorithms 4 SIAM Journal on Scientific Computing 4 Reliable Computing 3 Elektronische Rechenanlagen 3 Japan Journal of Industrial and Applied Mathematics 3 ELA. The Electronic Journal of Linear 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 Linear and Multilinear Algebra 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 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 122 Numerical analysis (65-XX) 40 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) 4 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 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 100 Publications have been cited 1,357 times in 769 Documents Cited by ▼ Year ▼ INTLAB – INTerval LABoratory. Zbl 0949.65046Rump, Siegfried M. 280 1999 Verification methods: rigorous results using floating-point arithmetic. Zbl 1323.65046Rump, Siegfried M. 125 2010 Accurate sum and dot product. Zbl 1084.65041Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 80 2005 Verification methods for dense and sparse systems of equations. Zbl 0813.65072Rump, S. M. 61 1994 Accurate floating-point summation. I: Faithful rounding. Zbl 1185.65082Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi 51 2008 Standardized notation in interval analysis. Zbl 1196.65088Kearfott, R. B.; Nakao, M. T.; Neumaier, A.; Rump, S. M.; Shary, S. P.; van Hentenryck, P. 32 2010 Kleine Fehlerschranken bei Matrixproblemen. Zbl 0437.65036Rump, Siegfried M. 30 1980 Fast and parallel interval arithmetic. Zbl 0942.65048Rump, Siegfried M. 29 1999 Structured perturbations. I: Normwise distances. Zbl 1061.15004Rump, Siegfried M. 26 2003 Eigenvalues, pseudospectrum and structured perturbations. Zbl 1093.15020Rump, Siegfried M. 25 2006 Computational error bounds for multiple or nearly multiple eigenvalues. Zbl 0986.65031Rump, Siegfried M. 23 2001 Accurate floating-point summation. II: Sign, \(K\)-fold faithful and rounding to nearest. Zbl 1190.65074Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi 23 2008 Improved error bounds for inner products in floating-point arithmetic. Zbl 1279.65052Jeannerod, Claude-Pierre; Rump, Siegfried M. 21 2013 Fast verification of solutions of matrix equations. Zbl 0999.65015Oishi, Shin’Ichi; Rump, Siegfried M. 20 2002 Theorems of Perron-Frobenius type for matrices without sign restrictions. Zbl 0901.15002Rump, S. M. 20 1997 Ten methods to bound multiple roots of polynomials. Zbl 1030.65046Rump, Siegfried M. 19 2003 Structured perturbations. II: Componentwise distances. Zbl 1061.15005Rump, Siegfried M. 19 2003 Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse. Zbl 1226.65028Rump, Siegfried M. 18 2011 On the solution of interval linear systems. Zbl 0753.65030Rump, S. M. 18 1992 Verification of positive definiteness. Zbl 1101.65039Rump, S. M. 17 2006 Inversion of extremely ill-conditioned matrices in floating-point. Zbl 1185.65050Rump, Siegfried M. 16 2009 A note on epsilon-inflation. Zbl 0920.65031Rump, Siegfried M. 15 1998 Verified error bounds for multiple roots of systems of nonlinear equations. Zbl 1201.65081Rump, Siegfried M.; Graillat, Stef 15 2010 Rigorous sensitivity analysis for systems of linear and nonlinear equations. Zbl 0701.65039Rump, Siegfried M. 15 1990 Solving nonlinear systems with least significant bit accuracy. Zbl 0485.65036Rump, S. M. 15 1982 Polynomial minimum root separation. Zbl 0405.12018Rump, Siegfried M. 13 1979 Rigorous solution of linear programming problems with uncertain data. Zbl 0735.90043Jansson, C.; Rump, S. M. 13 1991 Improved backward error bounds for LU and Cholesky factorizations. Zbl 1309.65031Rump, Siegfried M.; Jeannerod, Claude-Pierre 13 2014 Expansion and estimation of the range of bonlinear functions. Zbl 0853.65049Rump, S. M. 12 1996 Perron-Frobenius theory for complex matrices. Zbl 1019.15012Rump, Siegfried M. 12 2003 Ill-conditioned matrices are componentwise near to singularity. Zbl 0923.15003Rump, Siegfried M. 12 1999 Self-validating methods. Zbl 0978.65037Rump, Siegfried M. 12 2001 Ultimately fast accurate summation. Zbl 1202.65033Rump, Siegfried M. 11 2009 Bounds for the componentwise distance to the nearest singular matrix. Zbl 0870.65038Rump, S. M. 11 1997 Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications. Zbl 1244.65062Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shin’ichi; Rump, Siegfried M. 11 2012 On eigenvector bounds. Zbl 1042.65029Rump, Siegfried M.; Zemke, Jens-Peter M. 10 2003 Convergence of Rump’s method for inverting arbitrarily ill-conditioned matrices. Zbl 1120.65040Oishi, Shin’ichi; Tanabe, Kunio; Ogita, Takeshi; Rump, Siegfried M. 10 2007 Error estimation of floating-point summation and dot product. Zbl 1243.65047Rump, Siegfried M. 10 2012 Guaranteed inclusions for the complex generalized eigenproblem. Zbl 0676.65028Rump, S. M. 10 1989 Solving algebraic problems with high accuracy. Zbl 0597.65018Rump, Siegfried M. 10 1983 Verified bounds for least squares problems and underdetermined linear systems. Zbl 1255.65082Rump, Siegfried M. 8 2012 Validated solution of large linear systems. Zbl 0837.65013Rump, S. M. 8 1993 New results on verified inclusions. Zbl 0609.65033Rump, Siegfried M. 8 1986 FORTRAN-SC. A study of a FORTRAN extension for engineering/scientific computation with access to ACRITH. Zbl 0624.68032Bleher, J. H.; Rump, S. M.; Kulisch, U.; Metzger, M.; Ullrich, Ch.; Walter, W. 8 1987 Super-fast validated solution of linear systems. Zbl 1108.65020Rump, Siegfried M.; Ogita, Takeshi 7 2007 Almost sharp bounds for the componentwise distance to the nearest singular matrix. Zbl 0877.15030Rump, S. M. 7 1997 E-methods for fixed point equations f(x)=x. Zbl 0474.65039Kaucher, E.; Rump, S. M. 7 1982 A class of arbitrarily ill conditioned floating-point matrices. Zbl 0738.65042Rump, Siegfried M. 6 1991 Accurate solution of dense linear systems. II: Algorithms using directed rounding. Zbl 1260.65034Rump, Siegfried M. 6 2013 Accurate solution of dense linear systems I: Algorithms in rounding to nearest. Zbl 1255.65084Rump, Siegfried M. 5 2013 Small bounds for the solution of systems of linear equations. Zbl 0419.65023Rump, S. M.; Kaucher, E. 5 1980 Fast interval matrix multiplication. Zbl 1264.65065Rump, Siegfried M. 4 2012 On relative errors of floating-point operations: optimal bounds and applications. Zbl 1380.65082Jeannerod, Claude-Pierre; Rump, Siegfried M. 4 2018 Sharp estimates for perturbation errors in summations. Zbl 1453.65097Lange, Marko; Rump, Siegfried M. 4 2019 A method of obtaining verified solutions for linear systems suited for Java. Zbl 1108.65019Ozaki, K.; Ogita, T.; Miyajima, S.; Oishi, S.; Rump, S. M. 4 2007 On \(P\)-matrices. Zbl 1044.15013Rump, Siegfried M. 4 2003 Computing predecessor and successor in rounding to nearest. Zbl 1196.65089Rump, Siegfried M.; Zimmermann, Paul; Boldo, Sylvie; Melquiond, Guillaume 4 2009 Ill-conditionedness need not be componentwise near to ill-posedness for least squares problems. Zbl 0970.65039Rump, Siegfried M. 4 1999 Bounds for the determinant by Gershgorin circles. Zbl 1405.15011Rump, Siegfried M. 3 2019 Error estimates for the summation of real numbers with application to floating-point summation. Zbl 1380.65083Lange, Marko; Rump, Siegfried M. 3 2017 Improved componentwise verified error bounds for least squares problems and underdetermined linear systems. Zbl 1293.65062Rump, Siegfried M. 3 2014 Inclusion of zeros of nowhere differentiable \(n\)-dimensional functions. Zbl 0883.65041Rump, Siegfried M. 3 1997 Fast algorithms for floating-point interval matrix multiplication. Zbl 1248.65044Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 3 2012 The ratio between the Toeplitz and the unstructured condition number. Zbl 1203.15004Rump, Siegfried M.; Sekigawa, Hiroshi 3 2010 Optimal scaling for \(p\)-norms and componentwise distance to singularity. Zbl 1021.65023Rump, Siegfried M. 2 2003 Interval arithmetic over finitely many endpoints. Zbl 1264.65072Rump, Siegfried M. 2 2012 Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems. Zbl 0862.65033Rump, S. M. 2 1996 IEEE754 precision-\(k\) base-\(\beta\) arithmetic inherited by precision-\(m\) base-\(\beta\) arithmetic for \(k<m\). Zbl 1396.65177Rump, Siegfried M. 2 2017 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 1372.65140Rump, Siegfried Michael 2 2016 Improved error bounds for floating-point products and Horner’s scheme. Zbl 1342.65122Rump, Siegfried M.; Bünger, Florian; Jeannerod, Claude-Pierre 2 2016 Solution of linear and nonlinear algebraic problems with sharp, guaranteed bounds. Zbl 0548.65037Rump, S. M. 2 1984 Rigorous and portable standard functions. Zbl 0994.65017Rump, Siegfried M. 2 2001 Conservatism of the circle criterion – solution of a problem posed by A. Megretski: “How conservative is the circle criterion”. Zbl 1019.93046Rump, Siegfried M. 2 2001 Variational characterizations of the sign-real and the sign-complex spectral radius. Zbl 1046.15025Rump, Siegfried M. 2 2002 The determinant of a complex matrix and Gershgorin circles. Zbl 1430.15006Bünger, Florian; Rump, Siegfried M. 2 2019 The componentwise structured and unstructured backward errors can be arbitrarily far apart. Zbl 1328.65104Rump, Siegfried M. 2 2015 The sign-real spectral radius and cycle products. Zbl 0942.15005Rump, Siegfried M. 2 1998 Yet more elementary proofs that the determinant of a symplectic matrix is 1. Zbl 1352.15040Bünger, F.; Rump, S. M. 2 2017 Iterative refinement for ill-conditioned linear systems. Zbl 1188.65053Oishi, Shin’ichi; Ogita, Takeshi; Rump, Siegfried M. 2 2009 Algebraic computation, numerical computation and verified inclusions. Zbl 0663.65043Rump, Siegfried M. 2 1988 Algorithms for verified inclusions: Theory and practice. Zbl 0665.65046Rump, Siegfried M. 2 1988 Verified bounds for the determinant of real or complex point or interval matrices. Zbl 1437.65020Rump, Siegfried M. 1 2020 On recurrences converging to the wrong limit in finite precision and some new examples. Zbl 1448.65041Rump, Siegfried M. 1 2020 Lower bounds for the smallest singular value of certain Toeplitz-like triangular matrices with linearly increasing diagonal entries. Zbl 1423.15030Bünger, Florian; Rump, Siegfried M. 1 2019 Symbolic algebraic methods and verification methods. Zbl 0963.00018 1 2001 Verified solution of large linear and nonlinear systems. Zbl 0943.65039Rump, Siegfried M. 1 1999 Estimates of the determinant of a perturbed identity matrix. Zbl 1403.15003Rump, Siegfried M. 1 2018 Addendum to: “Estimates of the determinant of a perturbed identity matrix”. Zbl 1410.15017Rump, Siegfried M.; Batra, Prashant 1 2019 On the definition of unit roundoff. Zbl 1342.65123Rump, Siegfried M.; Lange, Marko 1 2016 Simple floating-point filters for the two-dimensional orientation problem. Zbl 1347.65050Ozaki, Katsuhisa; Bünger, Florian; Ogita, Takeshi; Oishi, Shin’ichi; Rump, Siegfried M. 1 2016 Arithmetic specification in FORTRAN 8X. Zbl 0553.68022Bohlender, 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 Solution of linear systems with verified accuracy. Zbl 0643.34014Rump, Siegfried M. 1 1987 Algorithms with result verification. – Some remarks on new developments. (Algorithmen mit Ergebnisverifikation. – Einige Bemerkungen zu neueren Entwicklungen.) Zbl 0812.65037Jansson, Christian; Rump, Siegfried M. 1 1994 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 Inclusion of the solution for large linear systems with \(M\)-matrix. Zbl 0829.65031Rump, Siegfried M. 1 1992 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 Adaptive and efficient algorithm for 2D orientation problem. Zbl 1185.65037Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 1 2009 FORTRAN-SC: A study of a FORTRAN extension for engineering/scientific computation with access to ACRITH. Zbl 0662.68010Bleher, J. H.; Rump, S. M.; Kulisch, U.; Metzger, M.; Ullrich, Ch.; Walter, W. 1 1988 Computer demonstration packages for standard problems of numerical mathematics. Zbl 0597.65017Rump, Siegfried M. 1 1983 Least significant bit evaluation of arithmetic expressions in single- precision. Zbl 0494.65020Rump, S. M.; Boehm, H. 1 1983 Verified bounds for the determinant of real or complex point or interval matrices. Zbl 1437.65020Rump, Siegfried M. 1 2020 On recurrences converging to the wrong limit in finite precision and some new examples. Zbl 1448.65041Rump, Siegfried M. 1 2020 Sharp estimates for perturbation errors in summations. Zbl 1453.65097Lange, Marko; Rump, Siegfried M. 4 2019 Bounds for the determinant by Gershgorin circles. Zbl 1405.15011Rump, Siegfried M. 3 2019 The determinant of a complex matrix and Gershgorin circles. Zbl 1430.15006Bünger, 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 1423.15030Bünger, Florian; Rump, Siegfried M. 1 2019 Addendum to: “Estimates of the determinant of a perturbed identity matrix”. Zbl 1410.15017Rump, Siegfried M.; Batra, Prashant 1 2019 On relative errors of floating-point operations: optimal bounds and applications. Zbl 1380.65082Jeannerod, Claude-Pierre; Rump, Siegfried M. 4 2018 Estimates of the determinant of a perturbed identity matrix. Zbl 1403.15003Rump, Siegfried M. 1 2018 Error estimates for the summation of real numbers with application to floating-point summation. Zbl 1380.65083Lange, Marko; Rump, Siegfried M. 3 2017 IEEE754 precision-\(k\) base-\(\beta\) arithmetic inherited by precision-\(m\) base-\(\beta\) arithmetic for \(k<m\). Zbl 1396.65177Rump, Siegfried M. 2 2017 Yet more elementary proofs that the determinant of a symplectic matrix is 1. Zbl 1352.15040Bünger, F.; Rump, S. M. 2 2017 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 1372.65140Rump, Siegfried Michael 2 2016 Improved error bounds for floating-point products and Horner’s scheme. Zbl 1342.65122Rump, Siegfried M.; Bünger, Florian; Jeannerod, Claude-Pierre 2 2016 On the definition of unit roundoff. Zbl 1342.65123Rump, Siegfried M.; Lange, Marko 1 2016 Simple floating-point filters for the two-dimensional orientation problem. Zbl 1347.65050Ozaki, Katsuhisa; Bünger, Florian; Ogita, Takeshi; Oishi, Shin’ichi; Rump, Siegfried M. 1 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 The componentwise structured and unstructured backward errors can be arbitrarily far apart. Zbl 1328.65104Rump, Siegfried M. 2 2015 Improved backward error bounds for LU and Cholesky factorizations. Zbl 1309.65031Rump, Siegfried M.; Jeannerod, Claude-Pierre 13 2014 Improved componentwise verified error bounds for least squares problems and underdetermined linear systems. Zbl 1293.65062Rump, Siegfried M. 3 2014 Improved error bounds for inner products in floating-point arithmetic. Zbl 1279.65052Jeannerod, Claude-Pierre; Rump, Siegfried M. 21 2013 Accurate solution of dense linear systems. II: Algorithms using directed rounding. Zbl 1260.65034Rump, Siegfried M. 6 2013 Accurate solution of dense linear systems I: Algorithms in rounding to nearest. Zbl 1255.65084Rump, Siegfried M. 5 2013 Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications. Zbl 1244.65062Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shin’ichi; Rump, Siegfried M. 11 2012 Error estimation of floating-point summation and dot product. Zbl 1243.65047Rump, Siegfried M. 10 2012 Verified bounds for least squares problems and underdetermined linear systems. Zbl 1255.65082Rump, Siegfried M. 8 2012 Fast interval matrix multiplication. Zbl 1264.65065Rump, Siegfried M. 4 2012 Fast algorithms for floating-point interval matrix multiplication. Zbl 1248.65044Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 3 2012 Interval arithmetic over finitely many endpoints. Zbl 1264.65072Rump, Siegfried M. 2 2012 Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse. Zbl 1226.65028Rump, Siegfried M. 18 2011 Verification methods: rigorous results using floating-point arithmetic. Zbl 1323.65046Rump, Siegfried M. 125 2010 Standardized notation in interval analysis. Zbl 1196.65088Kearfott, R. B.; Nakao, M. T.; Neumaier, A.; Rump, S. M.; Shary, S. P.; van Hentenryck, P. 32 2010 Verified error bounds for multiple roots of systems of nonlinear equations. Zbl 1201.65081Rump, Siegfried M.; Graillat, Stef 15 2010 The ratio between the Toeplitz and the unstructured condition number. Zbl 1203.15004Rump, Siegfried M.; Sekigawa, Hiroshi 3 2010 Inversion of extremely ill-conditioned matrices in floating-point. Zbl 1185.65050Rump, Siegfried M. 16 2009 Ultimately fast accurate summation. Zbl 1202.65033Rump, Siegfried M. 11 2009 Computing predecessor and successor in rounding to nearest. Zbl 1196.65089Rump, Siegfried M.; Zimmermann, Paul; Boldo, Sylvie; Melquiond, Guillaume 4 2009 Iterative refinement for ill-conditioned linear systems. Zbl 1188.65053Oishi, Shin’ichi; Ogita, Takeshi; Rump, Siegfried M. 2 2009 Adaptive and efficient algorithm for 2D orientation problem. Zbl 1185.65037Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 1 2009 Accurate floating-point summation. I: Faithful rounding. Zbl 1185.65082Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi 51 2008 Accurate floating-point summation. II: Sign, \(K\)-fold faithful and rounding to nearest. Zbl 1190.65074Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi 23 2008 Convergence of Rump’s method for inverting arbitrarily ill-conditioned matrices. Zbl 1120.65040Oishi, Shin’ichi; Tanabe, Kunio; Ogita, Takeshi; Rump, Siegfried M. 10 2007 Super-fast validated solution of linear systems. Zbl 1108.65020Rump, Siegfried M.; Ogita, Takeshi 7 2007 A method of obtaining verified solutions for linear systems suited for Java. Zbl 1108.65019Ozaki, 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 1093.15020Rump, Siegfried M. 25 2006 Verification of positive definiteness. Zbl 1101.65039Rump, S. M. 17 2006 Accurate sum and dot product. Zbl 1084.65041Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi 80 2005 Structured perturbations. I: Normwise distances. Zbl 1061.15004Rump, Siegfried M. 26 2003 Ten methods to bound multiple roots of polynomials. Zbl 1030.65046Rump, Siegfried M. 19 2003 Structured perturbations. II: Componentwise distances. Zbl 1061.15005Rump, Siegfried M. 19 2003 Perron-Frobenius theory for complex matrices. Zbl 1019.15012Rump, Siegfried M. 12 2003 On eigenvector bounds. Zbl 1042.65029Rump, Siegfried M.; Zemke, Jens-Peter M. 10 2003 On \(P\)-matrices. Zbl 1044.15013Rump, Siegfried M. 4 2003 Optimal scaling for \(p\)-norms and componentwise distance to singularity. Zbl 1021.65023Rump, Siegfried M. 2 2003 Fast verification of solutions of matrix equations. Zbl 0999.65015Oishi, Shin’Ichi; Rump, Siegfried M. 20 2002 Variational characterizations of the sign-real and the sign-complex spectral radius. Zbl 1046.15025Rump, Siegfried M. 2 2002 Computational error bounds for multiple or nearly multiple eigenvalues. Zbl 0986.65031Rump, Siegfried M. 23 2001 Self-validating methods. Zbl 0978.65037Rump, Siegfried M. 12 2001 Rigorous and portable standard functions. Zbl 0994.65017Rump, Siegfried M. 2 2001 Conservatism of the circle criterion – solution of a problem posed by A. Megretski: “How conservative is the circle criterion”. Zbl 1019.93046Rump, Siegfried M. 2 2001 Symbolic algebraic methods and verification methods. Zbl 0963.00018 1 2001 INTLAB – INTerval LABoratory. Zbl 0949.65046Rump, Siegfried M. 280 1999 Fast and parallel interval arithmetic. Zbl 0942.65048Rump, Siegfried M. 29 1999 Ill-conditioned matrices are componentwise near to singularity. Zbl 0923.15003Rump, Siegfried M. 12 1999 Ill-conditionedness need not be componentwise near to ill-posedness for least squares problems. Zbl 0970.65039Rump, Siegfried M. 4 1999 Verified solution of large linear and nonlinear systems. Zbl 0943.65039Rump, Siegfried M. 1 1999 A note on epsilon-inflation. Zbl 0920.65031Rump, Siegfried M. 15 1998 The sign-real spectral radius and cycle products. Zbl 0942.15005Rump, Siegfried M. 2 1998 Theorems of Perron-Frobenius type for matrices without sign restrictions. Zbl 0901.15002Rump, S. M. 20 1997 Bounds for the componentwise distance to the nearest singular matrix. Zbl 0870.65038Rump, S. M. 11 1997 Almost sharp bounds for the componentwise distance to the nearest singular matrix. Zbl 0877.15030Rump, S. M. 7 1997 Inclusion of zeros of nowhere differentiable \(n\)-dimensional functions. Zbl 0883.65041Rump, Siegfried M. 3 1997 Expansion and estimation of the range of bonlinear functions. Zbl 0853.65049Rump, S. M. 12 1996 Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems. Zbl 0862.65033Rump, S. M. 2 1996 Verification methods for dense and sparse systems of equations. Zbl 0813.65072Rump, S. M. 61 1994 Algorithms with result verification. – Some remarks on new developments. (Algorithmen mit Ergebnisverifikation. – Einige Bemerkungen zu neueren Entwicklungen.) Zbl 0812.65037Jansson, Christian; Rump, Siegfried M. 1 1994 Validated solution of large linear systems. Zbl 0837.65013Rump, S. M. 8 1993 On the solution of interval linear systems. Zbl 0753.65030Rump, S. M. 18 1992 Inclusion of the solution for large linear systems with \(M\)-matrix. Zbl 0829.65031Rump, Siegfried M. 1 1992 Rigorous solution of linear programming problems with uncertain data. Zbl 0735.90043Jansson, C.; Rump, S. M. 13 1991 A class of arbitrarily ill conditioned floating-point matrices. Zbl 0738.65042Rump, Siegfried M. 6 1991 Rigorous sensitivity analysis for systems of linear and nonlinear equations. Zbl 0701.65039Rump, Siegfried M. 15 1990 Guaranteed inclusions for the complex generalized eigenproblem. Zbl 0676.65028Rump, S. M. 10 1989 Algebraic computation, numerical computation and verified inclusions. Zbl 0663.65043Rump, Siegfried M. 2 1988 Algorithms for verified inclusions: Theory and practice. Zbl 0665.65046Rump, Siegfried M. 2 1988 FORTRAN-SC: A study of a FORTRAN extension for engineering/scientific computation with access to ACRITH. Zbl 0662.68010Bleher, 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 0624.68032Bleher, J. H.; Rump, S. M.; Kulisch, U.; Metzger, M.; Ullrich, Ch.; Walter, W. 8 1987 Solution of linear systems with verified accuracy. Zbl 0643.34014Rump, Siegfried M. 1 1987 New results on verified inclusions. Zbl 0609.65033Rump, Siegfried M. 8 1986 Solution of linear and nonlinear algebraic problems with sharp, guaranteed bounds. Zbl 0548.65037Rump, S. M. 2 1984 Arithmetic specification in FORTRAN 8X. Zbl 0553.68022Bohlender, 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 Solving algebraic problems with high accuracy. Zbl 0597.65018Rump, Siegfried M. 10 1983 Computer demonstration packages for standard problems of numerical mathematics. Zbl 0597.65017Rump, Siegfried M. 1 1983 Least significant bit evaluation of arithmetic expressions in single- precision. Zbl 0494.65020Rump, S. M.; Boehm, H. 1 1983 Solving nonlinear systems with least significant bit accuracy. Zbl 0485.65036Rump, S. M. 15 1982 E-methods for fixed point equations f(x)=x. Zbl 0474.65039Kaucher, E.; Rump, S. M. 7 1982 Kleine Fehlerschranken bei Matrixproblemen. Zbl 0437.65036Rump, Siegfried M. 30 1980 Small bounds for the solution of systems of linear equations. Zbl 0419.65023Rump, S. M.; Kaucher, E. 5 1980 Polynomial minimum root separation. Zbl 0405.12018Rump, Siegfried M. 13 1979 all cited Publications top 5 cited Publications all top 5 Cited by 885 Authors 55 Rump, Siegfried Michael 33 Nakao, Mitsuhiro T. 32 Oishi, Shin’ichi 30 Lessard, Jean-Philippe 30 Miyajima, Shinya 25 Ogita, Takeshi 22 Hladík, Milan 19 Mireles-James, Jason D. 19 Watanabe, Yoshitaka 15 Wei, Yimin 14 van den Berg, Jan Bouwe 13 Ozaki, Katsuhisa 12 Graillat, Stef 10 Kinoshita, Takehiko 9 Diao, Huaian 9 Jiang, Hao 9 Sharyĭ, Sergeĭ Petrovich 9 Tanaka, Kazuaki 8 Castelli, Roberto 8 Minamoto, Teruya 8 Plum, Michael 8 Takayasu, Akitoshi 8 Yamamoto, Nobito 7 Bünger, Florian 7 Cheng, Lizhi 7 Dehghani-Madiseh, Marzieh 7 Goldsztejn, Alexandre 7 Hashemi, Behnam 7 Kimura, Takuma 7 Liu, Xuefeng 7 Mayer, Günter 7 Nagatou, Kaori 7 Petković, Miodrag S. 7 Popova, Evgeniya D. 7 Skalna, Iwona 6 Breden, Maxime 6 Frommer, Andreas 6 Higham, Nicholas J. 6 Jeannerod, Claude-Pierre 6 Kearfott, Baker 6 Kolev, Lubomir V. 6 Li, Zhe 6 Wanner, Thomas 5 Alefeld, Götz E. 5 Dehghan Takht Fooladi, Mehdi 5 Eichfelder, Gabriele 5 Jaquette, Jonathan 5 Krämer, Walter 5 Li, Hanyu 5 Melquiond, Guillaume 5 Mizuguchi, Makoto 5 Muller, Jean-Michel 5 Neumaier, Arnold 5 Pan, Victor Yakovlevich 5 Pham Huu Anh Ngoc 5 Rohn, Jiri 5 Sekine, Kouta 4 Barrio, Roberto 4 Capinski, Maciej J. 4 Chen, Xiaojun 4 Church, Kevin E. M. 4 Csendes, Tibor 4 Domes, Ferenc 4 Du, Peibing 4 Gameiro, Marcio F. 4 Griewank, Andreas 4 Hashimoto, Kouji 4 Jansson, Christian 4 Kressner, Daniel 4 Lange, Marko 4 Mary, Theo A. 4 Mullen, Robert L. 4 Noschese, Silvia 4 Okamoto, Hisashi 4 Qian, Guoliang 4 Radons, Manuel 4 Roux, Pierre 4 Ryoo, Cheon Seoung 4 Schichl, Hermann 4 Zhi, Lihong 3 Adhikari, Bibhas 3 Aishima, Kensuke 3 Auer, Ekaterina 3 Boldo, Sylvie 3 Černý, Michal 3 Dobner, Hans-Jürgen 3 Eftekhari, Tahereh 3 Fernandes, Luiz Gustavo 3 Franek, Peter 3 García-Azpeitia, Carlos 3 Hartman, David 3 Jermann, Christophe 3 Kepley, Shane 3 Kolberg, Mariana Luderitz 3 Kreinovich, Vladik Yakovlevich 3 Kulisch, Ulrich W. 3 Lamour, René 3 Lang, Bruno 3 Liao, Xiangke 3 Louvet, Nicolas ...and 785 more Authors all top 5 Cited in 192 Serials 90 Journal of Computational and Applied Mathematics 60 Linear Algebra and its Applications 37 Computing 33 Japan Journal of Industrial and Applied Mathematics 32 Applied Mathematics and Computation 24 Numerical Algorithms 19 BIT 17 Reliable Computing 16 Journal of Global Optimization 14 Journal of Differential Equations 13 Computers & Mathematics with Applications 11 Numerische Mathematik 9 Mathematics of Computation 9 Theoretical Computer Science 9 Applied Numerical Mathematics 9 Journal of Symbolic Computation 9 Numerical Linear Algebra with Applications 8 SIAM Journal on Matrix Analysis and Applications 8 SIAM Journal on Scientific Computing 8 SIAM Journal on Applied Dynamical Systems 7 Automatica 7 Calcolo 6 Journal of Mathematical Analysis and Applications 6 Journal of Dynamics and Differential Equations 6 Communications in Nonlinear Science and Numerical Simulation 6 Journal of Computational Dynamics 5 Journal of Computational Physics 5 ELA. The Electronic Journal of Linear Algebra 5 Optimization Methods & Software 4 Linear and Multilinear Algebra 4 ACM Transactions on Mathematical Software 4 Physica D 4 Journal of Automated Reasoning 4 International Journal of Computer Mathematics 4 Mathematical Programming. Series A. Series B 4 Indagationes Mathematicae. New Series 4 Advances in Computational Mathematics 4 Soft Computing 4 Foundations of Computational Mathematics 4 Mathematics in Computer Science 4 Optimization Letters 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 Journal of Nonlinear Science 3 Formal Methods in System Design 3 Computational and Applied Mathematics 3 ETNA. Electronic Transactions on Numerical Analysis 3 Engineering Analysis with Boundary Elements 3 Constraints 3 Chaos 2 Artificial Intelligence 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of the Franklin Institute 2 Nonlinearity 2 Information Sciences 2 International Journal for Numerical Methods in Engineering 2 SIAM Journal on Numerical Analysis 2 Systems & Control Letters 2 Acta Applicandae Mathematicae 2 Discrete & Computational Geometry 2 Information and Computation 2 Applied Mathematics Letters 2 Computational Statistics 2 Applied Mathematical Modelling 2 European Journal of Operational Research 2 International Journal of Robust and Nonlinear Control 2 Discrete and Continuous Dynamical Systems 2 Mathematical Problems in Engineering 2 Journal of Inequalities and Applications 2 International Journal of Applied Mathematics and Computer Science 2 Methodology and Computing in Applied Probability 2 Journal of Applied Mathematics 2 Computational Methods for Differential Equations 1 American Mathematical Monthly 1 Archive for Rational Mechanics and Analysis 1 Computers and Fluids 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 1 Chaos, Solitons and Fractals 1 Acta Mathematica 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Czechoslovak Mathematical Journal 1 Fuzzy Sets and Systems 1 Journal of Computer and System Sciences 1 Journal of Geometry 1 Journal of Number Theory 1 Journal of Optimization Theory and Applications 1 Mathematische Nachrichten 1 Opsearch 1 Proceedings of the Japan Academy. Series A ...and 92 more Serials all top 5 Cited in 51 Fields 571 Numerical analysis (65-XX) 156 Linear and multilinear algebra; matrix theory (15-XX) 93 Partial differential equations (35-XX) 88 Operations research, mathematical programming (90-XX) 70 Computer science (68-XX) 56 Ordinary differential equations (34-XX) 44 Dynamical systems and ergodic theory (37-XX) 34 Operator theory (47-XX) 32 Systems theory; control (93-XX) 21 Fluid mechanics (76-XX) 17 Functions of a complex variable (30-XX) 17 Mechanics of deformable solids (74-XX) 15 Real functions (26-XX) 14 Field theory and polynomials (12-XX) 13 Mechanics of particles and systems (70-XX) 12 Statistics (62-XX) 11 Commutative algebra (13-XX) 11 Approximations and expansions (41-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 9 Probability theory and stochastic processes (60-XX) 8 Number theory (11-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Information and communication theory, circuits (94-XX) 6 Biology and other natural sciences (92-XX) 5 Combinatorics (05-XX) 5 Algebraic geometry (14-XX) 5 Special functions (33-XX) 5 Difference and functional equations (39-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Mathematical logic and foundations (03-XX) 4 Integral equations (45-XX) 4 Optics, electromagnetic theory (78-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Measure and integration (28-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Functional analysis (46-XX) 3 Convex and discrete geometry (52-XX) 3 Algebraic topology (55-XX) 3 Manifolds and cell complexes (57-XX) 2 Group theory and generalizations (20-XX) 2 Geometry (51-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 Differential geometry (53-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) Citations by Year