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Rump, Siegfried Michael

Author ID: rump.siegfried-michael Recent zbMATH articles by "Rump, Siegfried Michael"
Published as: Rump, Siegfried M.; Rump, S. M.; Rump, Siegfried; Rump, Siegfried Michael; Rump, S.
Homepage: https://www.tuhh.de/ti3/rump/
External Links: MGP · ORCID · Wikidata · ResearchGate · dblp

Publications by Year

Citations contained in zbMATH Open

110 Publications have been cited 1,672 times in 927 Documents Cited by Year
INTLAB – INTerval LABoratory. Zbl 0949.65046
Rump, Siegfried M.
356
1999
Verification methods: rigorous results using floating-point arithmetic. Zbl 1323.65046
Rump, Siegfried M.
149
2010
Accurate sum and dot product. Zbl 1084.65041
Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi
94
2005
Verification methods for dense and sparse systems of equations. Zbl 0813.65072
Rump, S. M.
69
1994
Accurate floating-point summation. I: Faithful rounding. Zbl 1185.65082
Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi
60
2008
Solving algebraic problems with high accuracy. Zbl 0597.65018
Rump, Siegfried M.
50
1983
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.
39
1980
Fast and parallel interval arithmetic. Zbl 0942.65048
Rump, Siegfried M.
31
1999
Structured perturbations. I: Normwise distances. Zbl 1061.15004
Rump, Siegfried M.
30
2003
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
Eigenvalues, pseudospectrum and structured perturbations. Zbl 1093.15020
Rump, Siegfried M.
27
2006
Structured perturbations. II: Componentwise distances. Zbl 1061.15005
Rump, Siegfried M.
24
2003
Improved error bounds for inner products in floating-point arithmetic. Zbl 1279.65052
Jeannerod, Claude-Pierre; Rump, Siegfried M.
24
2013
Verification of positive definiteness. Zbl 1101.65039
Rump, S. M.
23
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.
22
2009
Fast verification of solutions of matrix equations. Zbl 0999.65015
Oishi, Shin’Ichi; Rump, Siegfried M.
21
2002
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.
21
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 nonlinear systems with least significant bit accuracy. Zbl 0485.65036
Rump, S. M.
15
1982
Rigorous sensitivity analysis for systems of linear and nonlinear equations. Zbl 0701.65039
Rump, Siegfried M.
15
1990
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
Improved backward error bounds for LU and Cholesky factorizations. Zbl 1309.65031
Rump, Siegfried M.; Jeannerod, Claude-Pierre
15
2014
Polynomial minimum root separation. Zbl 0405.12018
Rump, Siegfried M.
14
1979
Perron-Frobenius theory for complex matrices. Zbl 1019.15012
Rump, Siegfried M.
14
2003
Ill-conditioned matrices are componentwise near to singularity. Zbl 0923.15003
Rump, Siegfried M.
14
1999
Rigorous solution of linear programming problems with uncertain data. Zbl 0735.90043
Jansson, C.; Rump, S. M.
13
1991
Error estimation of floating-point summation and dot product. Zbl 1243.65047
Rump, Siegfried M.
13
2012
Ultimately fast accurate summation. Zbl 1202.65033
Rump, Siegfried M.
13
2009
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
Self-validating methods. Zbl 0978.65037
Rump, Siegfried M.
12
2001
Guaranteed inclusions for the complex generalized eigenproblem. Zbl 0676.65028
Rump, S. M.
11
1989
On eigenvector bounds. Zbl 1042.65029
Rump, Siegfried M.; Zemke, Jens-Peter M.
11
2003
On relative errors of floating-point operations: optimal bounds and applications. Zbl 1380.65082
Jeannerod, Claude-Pierre; Rump, Siegfried M.
11
2018
New results on verified inclusions. Zbl 0609.65033
Rump, Siegfried M.
10
1986
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
Verified bounds for least squares problems and underdetermined linear systems. Zbl 1255.65082
Rump, Siegfried M.
9
2012
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
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
Accurate solution of dense linear systems. II: Algorithms using directed rounding. Zbl 1260.65034
Rump, Siegfried M.
8
2013
E-methods for fixed point equations f(x)=x. Zbl 0474.65039
Kaucher, E.; Rump, S. M.
7
1982
On \(P\)-matrices. Zbl 1044.15013
Rump, Siegfried M.
7
2003
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
Super-fast validated solution of linear systems. Zbl 1108.65020
Rump, Siegfried M.; Ogita, Takeshi
7
2007
A class of arbitrarily ill conditioned floating-point matrices. Zbl 0738.65042
Rump, Siegfried M.
6
1991
Accurate solution of dense linear systems I: Algorithms in rounding to nearest. Zbl 1255.65084
Rump, Siegfried M.
6
2013
Error estimates for the summation of real numbers with application to floating-point summation. Zbl 1380.65083
Lange, Marko; Rump, Siegfried M.
6
2017
Small bounds for the solution of systems of linear equations. Zbl 0419.65023
Rump, S. M.; Kaucher, E.
5
1980
Algorithms for verified inclusions: Theory and practice. Zbl 0665.65046
Rump, Siegfried M.
4
1988
Ill-conditionedness need not be componentwise near to ill-posedness for least squares problems. Zbl 0970.65039
Rump, Siegfried M.
4
1999
Fast algorithms for floating-point interval matrix multiplication. Zbl 1248.65044
Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi
4
2012
Fast interval matrix multiplication. Zbl 1264.65065
Rump, Siegfried M.
4
2012
The ratio between the Toeplitz and the unstructured condition number. Zbl 1203.15004
Rump, Siegfried M.; Sekigawa, Hiroshi
4
2010
Faithfully rounded floating-point computations. Zbl 1484.65350
Lange, Marko; Rump, Siegfried M.
4
2020
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
Inclusion of zeros of nowhere differentiable \(n\)-dimensional functions. Zbl 0883.65041
Rump, Siegfried M.
3
1997
Variational characterizations of the sign-real and the sign-complex spectral radius. Zbl 1046.15025
Rump, Siegfried M.
3
2002
Rigorous and portable standard functions. Zbl 0994.65017
Rump, Siegfried M.
3
2001
The sign-real spectral radius and cycle products. Zbl 0942.15005
Rump, Siegfried M.
3
1998
Algebraic computation, numerical computation and verified inclusions. Zbl 0663.65043
Rump, Siegfried M.
3
1988
Iterative refinement for ill-conditioned linear systems. Zbl 1188.65053
Oishi, Shin’ichi; Ogita, Takeshi; Rump, Siegfried M.
3
2009
IEEE754 precision-\(k\) base-\(\beta\) arithmetic inherited by precision-\(m\) base-\(\beta\) arithmetic for \(k<m\). Zbl 1396.65177
Rump, Siegfried M.
3
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
Bounds for the determinant by Gershgorin circles. Zbl 1405.15011
Rump, Siegfried M.
3
2019
Improved componentwise verified error bounds for least squares problems and underdetermined linear systems. Zbl 1293.65062
Rump, Siegfried M.
3
2014
Solution of linear and nonlinear algebraic problems with sharp, guaranteed bounds. Zbl 0548.65037
Rump, S. M.
2
1984
Optimal scaling for \(p\)-norms and componentwise distance to singularity. Zbl 1021.65023
Rump, Siegfried M.
2
2003
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
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
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
On recurrences converging to the wrong limit in finite precision and some new examples. Zbl 1448.65041
Rump, Siegfried M.
2
2020
The determinant of a complex matrix and Gershgorin circles. Zbl 1430.15006
Bünger, Florian; Rump, Siegfried M.
2
2019
Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems. Zbl 0862.65033
Rump, S. M.
2
1996
Yet more elementary proofs that the determinant of a symplectic matrix is 1. Zbl 1352.15040
Bünger, F.; Rump, S. M.
2
2017
The componentwise structured and unstructured backward errors can be arbitrarily far apart. Zbl 1328.65104
Rump, Siegfried M.
2
2015
Solution of linear systems with verified accuracy. Zbl 0643.34014
Rump, Siegfried M.
1
1987
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
Least significant bit evaluation of arithmetic expressions in single- precision. Zbl 0494.65020
Rump, S. M.; Boehm, H.
1
1983
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
Verified solution of large linear and nonlinear systems. Zbl 0943.65039
Rump, Siegfried M.
1
1999
Symbolic algebraic methods and verification methods. Zbl 0963.00018
1
2001
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
Computer demonstration packages for standard problems of numerical mathematics. Zbl 0597.65017
Rump, Siegfried M.
1
1983
Adaptive and efficient algorithm for 2D orientation problem. Zbl 1185.65037
Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi
1
2009
Towards optimal use of multi-precision arithmetic: a remark. Zbl 1098.65046
Kreinovich, Vladik; Rump, Siegfried
1
2006
Accurate and reliable computing in floating-point arithmetic. Zbl 1295.65133
Rump, Siegfried M.
1
2010
Addendum to: “On recurrences converging to the wrong limit in finite precision and some new examples”. Zbl 1456.65031
Rump, Siegfried M.
1
2020
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
Verified error bounds for all eigenvalues and eigenvectors of a matrix. Zbl 1508.65034
Rump, Siegfried M.
1
2022
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 error bounds for all eigenvalues and eigenvectors of a matrix. Zbl 1508.65034
Rump, Siegfried M.
1
2022
Convergence results for some piecewise linear solvers. Zbl 1493.90207
Radons, Manuel; 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&rsquo;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&rsquo;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
15
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.
24
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&rsquo;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.
9
2012
Fast algorithms for floating-point interval matrix multiplication. Zbl 1248.65044
Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin&rsquo;ichi
4
2012
Fast interval matrix multiplication. Zbl 1264.65065
Rump, Siegfried M.
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.
21
2011
Verification methods: rigorous results using floating-point arithmetic. Zbl 1323.65046
Rump, Siegfried M.
149
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
Accurate and reliable computing in floating-point arithmetic. Zbl 1295.65133
Rump, Siegfried M.
1
2010
Inversion of extremely ill-conditioned matrices in floating-point. Zbl 1185.65050
Rump, Siegfried M.
22
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&rsquo;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&rsquo;ichi
1
2009
Accurate floating-point summation. I: Faithful rounding. Zbl 1185.65082
Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin&rsquo;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&rsquo;ichi
29
2008
Convergence of Rump’s method for inverting arbitrarily ill-conditioned matrices. Zbl 1120.65040
Oishi, Shin&rsquo;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.
27
2006
Verification of positive definiteness. Zbl 1101.65039
Rump, S. M.
23
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&rsquo;ichi
94
2005
Structured perturbations. I: Normwise distances. Zbl 1061.15004
Rump, Siegfried M.
30
2003
Structured perturbations. II: Componentwise distances. Zbl 1061.15005
Rump, Siegfried M.
24
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.
11
2003
On \(P\)-matrices. Zbl 1044.15013
Rump, Siegfried M.
7
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&rsquo;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.
356
1999
Fast and parallel interval arithmetic. Zbl 0942.65048
Rump, Siegfried M.
31
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.
69
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.
4
1988
Algebraic computation, numerical computation and verified inclusions. Zbl 0663.65043
Rump, Siegfried M.
3
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.
10
1986
...and 10 more Documents
all top 5

Cited by 1,077 Authors

60 Rump, Siegfried Michael
37 Nakao, Mitsuhiro T.
35 Oishi, Shin’ichi
34 Lessard, Jean-Philippe
33 Miyajima, Shinya
28 Hladík, Milan
27 Ogita, Takeshi
25 Watanabe, Yoshitaka
23 Mireles-James, Jason D.
17 Wei, Yimin
16 Graillat, Stef
16 Ozaki, Katsuhisa
14 van den Berg, Jan Bouwe
12 Kinoshita, Takehiko
11 Diao, Huaian
11 Jiang, Hao
10 Neumaier, Arnold
10 Ryoo, Cheon Seoung
10 Sharyĭ, Sergeĭ Petrovich
10 Takayasu, Akitoshi
10 Tanaka, Kazuaki
10 Yamamoto, Nobito
9 Breden, Maxime
9 Bünger, Florian
9 Plum, Michael
9 Wanner, Thomas
8 Castelli, Roberto
8 Dehghani-Madiseh, Marzieh
8 Hashemi, Behnam
8 Liu, Xuefeng
8 Minamoto, Teruya
8 Muller, Jean-Michel
8 Nagatou, Kaori
8 Popova, Evgeniya D.
8 Skalna, Iwona
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 Mizuguchi, Makoto
7 Petković, Miodrag S.
7 Rohn, Jiri
6 Barrio, Roberto
6 Capinski, Maciej J.
6 Church, Kevin E. M.
6 Eichfelder, Gabriele
6 Frommer, Andreas
6 Jaquette, Jonathan
6 Kearfott, Baker
6 Kolev, Lubomir V.
6 Li, Zhe
6 Mary, Theo A.
6 Schichl, Hermann
6 Sekine, Kouta
5 Alefeld, Götz E.
5 Boldo, Sylvie
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 Sander, Evelyn
5 Zhi, Lihong
4 Auer, Ekaterina
4 Chen, Xiaojun
4 Cheng, Jinsan
4 Csendes, Tibor
4 Dobner, Hans-Jürgen
4 Gameiro, Marcio F.
4 Griewank, Andreas
4 Hashimoto, Kouji
4 Jansson, Christian
4 Kepley, Shane
4 Kubica, Bartłomiej Jacek
4 Miyaji, Tomoyuki
4 Mullen, Robert L.
4 Okamoto, Hisashi
4 Qian, Guoliang
4 Qiao, Sanzheng
4 Rauh, Andreas
4 Roy, Falguni
4 Semisalov, Boris Vladimirovich
4 Tsigaridas, Elias P.
3 Adhikari, Bibhas
3 Aishima, Kensuke
3 Cai, Shuting
3 Černý, Michal
3 Cucker, Felipe
3 Eftekhari, Tahereh
3 Fernandes, Luiz Gustavo
...and 977 more Authors
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Cited in 221 Serials

96 Journal of Computational and Applied Mathematics
64 Linear Algebra and its Applications
39 Japan Journal of Industrial and Applied Mathematics
37 Computing
36 Applied Mathematics and Computation
28 Numerical Algorithms
23 BIT
21 Journal of Global Optimization
17 Journal of Differential Equations
17 Reliable Computing
15 Computers & Mathematics with Applications
13 SIAM Journal on Matrix Analysis and Applications
12 Numerische Mathematik
12 Journal of Symbolic Computation
12 Numerical Linear Algebra with Applications
11 SIAM Journal on Applied Dynamical Systems
10 Mathematics of Computation
10 Theoretical Computer Science
10 Applied Numerical Mathematics
10 Communications in Nonlinear Science and Numerical Simulation
9 SIAM Journal on Scientific Computing
8 Automatica
7 Calcolo
7 Journal of Automated Reasoning
7 Journal of Dynamics and Differential Equations
7 ELA. The Electronic Journal of Linear Algebra
7 Journal of Computational Dynamics
6 Journal of Mathematical Analysis and Applications
6 ACM Transactions on Mathematical Software
5 Journal of Computational Physics
5 Linear and Multilinear Algebra
5 Mathematical Programming. Series A. Series B
5 Computational and Applied Mathematics
5 Optimization Methods & Software
5 Soft Computing
5 Mathematics in Computer Science
5 Optimization Letters
4 Nonlinearity
4 SIAM Journal on Numerical Analysis
4 Physica D
4 International Journal of Computer Mathematics
4 Indagationes Mathematicae. New Series
4 International Journal of Robust and Nonlinear Control
4 ETNA. Electronic Transactions on Numerical Analysis
4 Advances in Computational Mathematics
4 Foundations of Computational Mathematics
4 Journal of Mathematical Modeling
3 Computer Methods in Applied Mechanics and Engineering
3 Information Sciences
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 Applied Mathematics Letters
3 Mathematical and Computer Modelling
3 Applications of Mathematics
3 Celestial Mechanics and Dynamical Astronomy
3 Applicable Algebra in Engineering, Communication and Computing
3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
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
3 JSIAM Letters
2 Artificial Intelligence
2 Archive for Rational Mechanics and Analysis
2 Communications on Pure and Applied Mathematics
2 Journal of the Franklin Institute
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 Journal of Scientific Computing
2 Computational Statistics
2 Computational Mathematics and Mathematical Physics
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 S\(\vec{\text{e}}\)MA Journal
2 Computational Methods for Differential Equations
1 American Mathematical Monthly
1 Computers and Fluids
1 Computer Physics Communications
1 General Relativity and Gravitation
1 International Journal for Numerical and Analytical Methods in Geomechanics
1 Inverse Problems
...and 121 more Serials
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Cited in 52 Fields

673 Numerical analysis (65-XX)
182 Linear and multilinear algebra; matrix theory (15-XX)
118 Partial differential equations (35-XX)
109 Operations research, mathematical programming (90-XX)
91 Computer science (68-XX)
64 Ordinary differential equations (34-XX)
55 Dynamical systems and ergodic theory (37-XX)
43 Systems theory; control (93-XX)
41 Operator theory (47-XX)
27 Fluid mechanics (76-XX)
21 Mechanics of deformable solids (74-XX)
19 Mechanics of particles and systems (70-XX)
17 Functions of a complex variable (30-XX)
17 Calculus of variations and optimal control; optimization (49-XX)
16 Real functions (26-XX)
16 Statistics (62-XX)
15 Field theory and polynomials (12-XX)
15 Approximations and expansions (41-XX)
13 Commutative algebra (13-XX)
13 Probability theory and stochastic processes (60-XX)
10 Number theory (11-XX)
10 Algebraic geometry (14-XX)
10 Special functions (33-XX)
8 Information and communication theory, circuits (94-XX)
7 Global analysis, analysis on manifolds (58-XX)
7 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
7 Biology and other natural sciences (92-XX)
6 Mathematical logic and foundations (03-XX)
6 Combinatorics (05-XX)
6 Functional analysis (46-XX)
5 Difference and functional equations (39-XX)
5 Harmonic analysis on Euclidean spaces (42-XX)
5 Integral equations (45-XX)
5 Optics, electromagnetic theory (78-XX)
4 Convex and discrete geometry (52-XX)
4 Manifolds and cell complexes (57-XX)
4 Statistical mechanics, structure of matter (82-XX)
3 Measure and integration (28-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)

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