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Rump, Siegfried Michael

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Author ID: rump.siegfried-michael Recent zbMATH articles by "Rump, Siegfried Michael"
Published as: Rump, S.; Rump, S. M.; Rump, Siegfried; Rump, Siegfried M.; Rump, Siegfried Michael
Documents Indexed: 138 Publications since 1979, including 5 Books

Publications by Year

Citations contained in zbMATH

97 Publications have been cited 1,170 times in 666 Documents Cited by Year
INTLAB – INTerval LABoratory. Zbl 0949.65046
Rump, Siegfried M.
221
1999
Verification methods: rigorous results using floating-point arithmetic. Zbl 1323.65046
Rump, Siegfried M.
94
2010
Accurate sum and dot product. Zbl 1084.65041
Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi
67
2005
Verification methods for dense and sparse systems of equations. Zbl 0813.65072
Rump, S. M.
59
1994
Accurate floating-point summation. I: Faithful rounding. Zbl 1185.65082
Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi
42
2008
Kleine Fehlerschranken bei Matrixproblemen. Zbl 0437.65036
Rump, Siegfried M.
29
1980
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.
28
2010
Fast and parallel interval arithmetic. Zbl 0942.65048
Rump, Siegfried M.
28
1999
Structured perturbations. I: Normwise distances. Zbl 1061.15004
Rump, Siegfried M.
26
2003
Solving algebraic problems with high accuracy. Zbl 0597.65018
Rump, Siegfried M.
24
1983
Eigenvalues, pseudospectrum and structured perturbations. Zbl 1093.15020
Rump, Siegfried M.
21
2006
Accurate floating-point summation. II: Sign, \(K\)-fold faithful and rounding to nearest. Zbl 1190.65074
Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi
20
2008
Computational error bounds for multiple or nearly multiple eigenvalues. Zbl 0986.65031
Rump, Siegfried M.
20
2001
Structured perturbations. II: Componentwise distances. Zbl 1061.15005
Rump, Siegfried M.
19
2003
Ten methods to bound multiple roots of polynomials. Zbl 1030.65046
Rump, Siegfried M.
19
2003
Fast verification of solutions of matrix equations. Zbl 0999.65015
Oishi, Shin’Ichi; Rump, Siegfried M.
19
2002
On the solution of interval linear systems. Zbl 0753.65030
Rump, S. M.
19
1992
Theorems of Perron-Frobenius type for matrices without sign restrictions. Zbl 0901.15002
Rump, S. M.
18
1997
Verification of positive definiteness. Zbl 1101.65039
Rump, S. M.
15
2006
Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse. Zbl 1226.65028
Rump, Siegfried M.
14
2011
A note on epsilon-inflation. Zbl 0920.65031
Rump, Siegfried M.
14
1998
Rigorous sensitivity analysis for systems of linear and nonlinear equations. Zbl 0701.65039
Rump, Siegfried M.
14
1990
Solving nonlinear systems with least significant bit accuracy. Zbl 0485.65036
Rump, S. M.
14
1982
Improved error bounds for inner products in floating-point arithmetic. Zbl 1279.65052
Jeannerod, Claude-Pierre; Rump, Siegfried M.
13
2013
Inversion of extremely ill-conditioned matrices in floating-point. Zbl 1185.65050
Rump, Siegfried M.
12
2009
Self-validating methods. Zbl 0978.65037
Rump, Siegfried M.
12
2001
Polynomial minimum root separation. Zbl 0405.12018
Rump, Siegfried M.
12
1979
Verified error bounds for multiple roots of systems of nonlinear equations. Zbl 1201.65081
Rump, Siegfried M.; Graillat, Stef
11
2010
Perron-Frobenius theory for complex matrices. Zbl 1019.15012
Rump, Siegfried M.
11
2003
Expansion and estimation of the range of bonlinear functions. Zbl 0853.65049
Rump, S. M.
11
1996
Improved backward error bounds for LU and Cholesky factorizations. Zbl 1309.65031
Rump, Siegfried M.; Jeannerod, Claude-Pierre
10
2014
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.
10
2012
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
Ill-conditioned matrices are componentwise near to singularity. Zbl 0923.15003
Rump, Siegfried M.
10
1999
Bounds for the componentwise distance to the nearest singular matrix. Zbl 0870.65038
Rump, S. M.
10
1997
Rigorous solution of linear programming problems with uncertain data. Zbl 0735.90043
Jansson, C.; Rump, S. M.
10
1991
Guaranteed inclusions for the complex generalized eigenproblem. Zbl 0676.65028
Rump, S. M.
9
1989
Error estimation of floating-point summation and dot product. Zbl 1243.65047
Rump, Siegfried M.
8
2012
Ultimately fast accurate summation. Zbl 1202.65033
Rump, Siegfried M.
8
2009
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
New results on verified inclusions. Zbl 0609.65033
Rump, Siegfried M.
8
1986
Verified bounds for least squares problems and underdetermined linear systems. Zbl 1255.65082
Rump, Siegfried M.
7
2012
On eigenvector bounds. Zbl 1042.65029
Rump, Siegfried M.; Zemke, Jens-Peter M.
7
2003
E-methods for fixed point equations f(x)=x. Zbl 0474.65039
Kaucher, E.; Rump, S. M.
7
1982
Super-fast validated solution of linear systems. Zbl 1108.65020
Rump, Siegfried M.; Ogita, Takeshi
6
2007
Almost sharp bounds for the componentwise distance to the nearest singular matrix. Zbl 0877.15030
Rump, S. M.
6
1997
A class of arbitrarily ill conditioned floating-point matrices. Zbl 0738.65042
Rump, Siegfried M.
5
1991
Small bounds for the solution of systems of linear equations. Zbl 0419.65023
Rump, S. M.; Kaucher, E.
5
1980
Accurate solution of dense linear systems I: Algorithms in rounding to nearest. Zbl 1255.65084
Rump, Siegfried M.
4
2013
Fast interval matrix multiplication. Zbl 1264.65065
Rump, Siegfried M.
4
2012
On \(P\)-matrices. Zbl 1044.15013
Rump, Siegfried M.
4
2003
Ill-conditionedness need not be componentwise near to ill-posedness for least squares problems. Zbl 0970.65039
Rump, Siegfried M.
4
1999
Bounds for the determinant by Gershgorin circles. Zbl 1405.15011
Rump, Siegfried M.
3
2019
Sharp estimates for perturbation errors in summations. Zbl 1453.65097
Lange, Marko; 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
Accurate solution of dense linear systems. II: Algorithms using directed rounding. Zbl 1260.65034
Rump, Siegfried M.
3
2013
Fast algorithms for floating-point interval matrix multiplication. Zbl 1248.65044
Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi
3
2012
The ratio between the Toeplitz and the unstructured condition number. Zbl 1203.15004
Rump, Siegfried M.; Sekigawa, Hiroshi
3
2010
Computing predecessor and successor in rounding to nearest. Zbl 1196.65089
Rump, Siegfried M.; Zimmermann, Paul; Boldo, Sylvie; Melquiond, Guillaume
3
2009
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.
3
2007
Inclusion of zeros of nowhere differentiable \(n\)-dimensional functions. Zbl 0883.65041
Rump, Siegfried M.
3
1997
The determinant of a complex matrix and Gershgorin circles. Zbl 1430.15006
Bünger, Florian; Rump, Siegfried M.
2
2019
On relative errors of floating-point operations: optimal bounds and applications. Zbl 1380.65082
Jeannerod, Claude-Pierre; Rump, Siegfried M.
2
2018
IEEE754 precision-\(k\) base-\(\beta\) arithmetic inherited by precision-\(m\) base-\(\beta\) arithmetic for \(k<m\). Zbl 1396.65177
Rump, Siegfried 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
2
2016
The componentwise structured and unstructured backward errors can be arbitrarily far apart. Zbl 1328.65104
Rump, Siegfried M.
2
2015
Iterative refinement for ill-conditioned linear systems. Zbl 1188.65053
Oishi, Shin’ichi; Ogita, Takeshi; Rump, Siegfried M.
2
2009
Optimal scaling for \(p\)-norms and componentwise distance to singularity. Zbl 1021.65023
Rump, Siegfried M.
2
2003
Variational characterizations of the sign-real and the sign-complex spectral radius. Zbl 1046.15025
Rump, Siegfried M.
2
2002
Rigorous and portable standard functions. Zbl 0994.65017
Rump, Siegfried M.
2
2001
The sign-real spectral radius and cycle products. Zbl 0942.15005
Rump, Siegfried M.
2
1998
Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems. Zbl 0862.65033
Rump, S. M.
2
1996
Algorithms for verified inclusions: Theory and practice. Zbl 0665.65046
Rump, Siegfried M.
2
1988
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
On recurrences converging to the wrong limit in finite precision and some new examples. Zbl 1448.65041
Rump, Siegfried M.
1
2020
Addendum to: “Estimates of the determinant of a perturbed identity matrix”. Zbl 1410.15017
Rump, Siegfried M.; Batra, Prashant
1
2019
Estimates of the determinant of a perturbed identity matrix. Zbl 1403.15003
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.
1
2017
Yet more elementary proofs that the determinant of a symplectic matrix is 1. Zbl 1352.15040
Bünger, F.; Rump, S. M.
1
2017
Floating-point arithmetic on the test bench. How are verified numerical solutions calculated? Zbl 1372.65140
Rump, Siegfried Michael
1
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.
1
2016
On the definition of unit roundoff. Zbl 1342.65123
Rump, Siegfried M.; Lange, Marko
1
2016
Adaptive and efficient algorithm for 2D orientation problem. Zbl 1185.65037
Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi
1
2009
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
Alefeld, Götz (ed.); Nakao, Mitsuhiro (ed.); Rump, Siegfried M. (ed.)
1
2007
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.
1
2001
Symbolic algebraic methods and verification methods. Zbl 0963.00018
Alefeld, Götz (ed.); Rohn, Jiří (ed.); Rump, Siegfried (ed.); Yamamoto, Tetsuro (ed.)
1
2001
Verified solution of large linear and nonlinear systems. Zbl 0943.65039
Rump, Siegfried M.
1
1999
Verified solution of large systems and global optimization problems. Zbl 0866.65035
Rump, Siegfried M.
1
1995
Algorithms with result verification. – Some remarks on new developments. Zbl 0812.65037
Jansson, Christian; Rump, Siegfried M.
1
1994
Inclusion of the solution for large linear systems with \(M\)-matrix. Zbl 0829.65031
Rump, Siegfried M.
1
1992
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
Solution of linear systems with verified accuracy. Zbl 0643.34014
Rump, Siegfried M.
1
1987
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
Least significant bit evaluation of arithmetic expressions in single- precision. Zbl 0494.65020
Rump, S. M.; Boehm, H.
1
1983
On recurrences converging to the wrong limit in finite precision and some new examples. Zbl 1448.65041
Rump, Siegfried M.
1
2020
Bounds for the determinant by Gershgorin circles. Zbl 1405.15011
Rump, Siegfried M.
3
2019
Sharp estimates for perturbation errors in summations. Zbl 1453.65097
Lange, Marko; Rump, Siegfried M.
3
2019
The determinant of a complex matrix and Gershgorin circles. Zbl 1430.15006
Bünger, Florian; Rump, Siegfried M.
2
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.
2
2018
Estimates of the determinant of a perturbed identity matrix. Zbl 1403.15003
Rump, Siegfried M.
1
2018
IEEE754 precision-\(k\) base-\(\beta\) arithmetic inherited by precision-\(m\) base-\(\beta\) arithmetic for \(k<m\). Zbl 1396.65177
Rump, Siegfried M.
2
2017
Error estimates for the summation of real numbers with application to floating-point summation. Zbl 1380.65083
Lange, Marko; Rump, Siegfried M.
1
2017
Yet more elementary proofs that the determinant of a symplectic matrix is 1. Zbl 1352.15040
Bünger, F.; Rump, S. M.
1
2017
Improved error bounds for floating-point products and Horner’s scheme. Zbl 1342.65122
Rump, Siegfried M.; Bünger, Florian; Jeannerod, Claude-Pierre
2
2016
Floating-point arithmetic on the test bench. How are verified numerical solutions calculated? Zbl 1372.65140
Rump, Siegfried Michael
1
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.
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
10
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.
13
2013
Accurate solution of dense linear systems I: Algorithms in rounding to nearest. Zbl 1255.65084
Rump, Siegfried M.
4
2013
Accurate solution of dense linear systems. II: Algorithms using directed rounding. Zbl 1260.65034
Rump, Siegfried M.
3
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.
10
2012
Error estimation of floating-point summation and dot product. Zbl 1243.65047
Rump, Siegfried M.
8
2012
Verified bounds for least squares problems and underdetermined linear systems. Zbl 1255.65082
Rump, Siegfried M.
7
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
3
2012
Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse. Zbl 1226.65028
Rump, Siegfried M.
14
2011
Verification methods: rigorous results using floating-point arithmetic. Zbl 1323.65046
Rump, Siegfried M.
94
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.
28
2010
Verified error bounds for multiple roots of systems of nonlinear equations. Zbl 1201.65081
Rump, Siegfried M.; Graillat, Stef
11
2010
The ratio between the Toeplitz and the unstructured condition number. Zbl 1203.15004
Rump, Siegfried M.; Sekigawa, Hiroshi
3
2010
Inversion of extremely ill-conditioned matrices in floating-point. Zbl 1185.65050
Rump, Siegfried M.
12
2009
Ultimately fast accurate summation. Zbl 1202.65033
Rump, Siegfried M.
8
2009
Computing predecessor and successor in rounding to nearest. Zbl 1196.65089
Rump, Siegfried M.; Zimmermann, Paul; Boldo, Sylvie; Melquiond, Guillaume
3
2009
Iterative refinement for ill-conditioned linear systems. Zbl 1188.65053
Oishi, Shin’ichi; Ogita, Takeshi; Rump, Siegfried M.
2
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
42
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
20
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
6
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.
3
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
Alefeld, Götz (ed.); Nakao, Mitsuhiro (ed.); Rump, Siegfried M. (ed.)
1
2007
Eigenvalues, pseudospectrum and structured perturbations. Zbl 1093.15020
Rump, Siegfried M.
21
2006
Verification of positive definiteness. Zbl 1101.65039
Rump, S. M.
15
2006
Accurate sum and dot product. Zbl 1084.65041
Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi
67
2005
Structured perturbations. I: Normwise distances. Zbl 1061.15004
Rump, Siegfried M.
26
2003
Structured perturbations. II: Componentwise distances. Zbl 1061.15005
Rump, Siegfried M.
19
2003
Ten methods to bound multiple roots of polynomials. Zbl 1030.65046
Rump, Siegfried M.
19
2003
Perron-Frobenius theory for complex matrices. Zbl 1019.15012
Rump, Siegfried M.
11
2003
On eigenvector bounds. Zbl 1042.65029
Rump, Siegfried M.; Zemke, Jens-Peter M.
7
2003
On \(P\)-matrices. Zbl 1044.15013
Rump, Siegfried M.
4
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.
19
2002
Variational characterizations of the sign-real and the sign-complex spectral radius. Zbl 1046.15025
Rump, Siegfried M.
2
2002
Computational error bounds for multiple or nearly multiple eigenvalues. Zbl 0986.65031
Rump, Siegfried M.
20
2001
Self-validating methods. Zbl 0978.65037
Rump, Siegfried M.
12
2001
Rigorous and portable standard functions. Zbl 0994.65017
Rump, Siegfried M.
2
2001
Conservatism of the circle criterion – solution of a problem posed by A. Megretski: “How conservative is the circle criterion”. Zbl 1019.93046
Rump, Siegfried M.
1
2001
Symbolic algebraic methods and verification methods. Zbl 0963.00018
Alefeld, Götz (ed.); Rohn, Jiří (ed.); Rump, Siegfried (ed.); Yamamoto, Tetsuro (ed.)
1
2001
INTLAB – INTerval LABoratory. Zbl 0949.65046
Rump, Siegfried M.
221
1999
Fast and parallel interval arithmetic. Zbl 0942.65048
Rump, Siegfried M.
28
1999
Ill-conditioned matrices are componentwise near to singularity. Zbl 0923.15003
Rump, Siegfried M.
10
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.
14
1998
The sign-real spectral radius and cycle products. Zbl 0942.15005
Rump, Siegfried M.
2
1998
Theorems of Perron-Frobenius type for matrices without sign restrictions. Zbl 0901.15002
Rump, S. M.
18
1997
Bounds for the componentwise distance to the nearest singular matrix. Zbl 0870.65038
Rump, S. M.
10
1997
Almost sharp bounds for the componentwise distance to the nearest singular matrix. Zbl 0877.15030
Rump, S. M.
6
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.
11
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.
59
1994
Algorithms with result verification. – Some remarks on new developments. 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.
10
1991
A class of arbitrarily ill conditioned floating-point matrices. Zbl 0738.65042
Rump, Siegfried M.
5
1991
Rigorous sensitivity analysis for systems of linear and nonlinear equations. Zbl 0701.65039
Rump, Siegfried M.
14
1990
Guaranteed inclusions for the complex generalized eigenproblem. Zbl 0676.65028
Rump, S. M.
9
1989
Algorithms for verified inclusions: Theory and practice. Zbl 0665.65046
Rump, Siegfried M.
2
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.
8
1986
Solution of linear and nonlinear algebraic problems with sharp, guaranteed bounds. Zbl 0548.65037
Rump, S. M.
2
1984
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
Solving algebraic problems with high accuracy. Zbl 0597.65018
Rump, Siegfried M.
24
1983
Computer demonstration packages for standard problems of numerical mathematics. Zbl 0597.65017
Rump, Siegfried M.
1
1983
Least significant bit evaluation of arithmetic expressions in single- precision. Zbl 0494.65020
Rump, S. M.; Boehm, H.
1
1983
Solving nonlinear systems with least significant bit accuracy. Zbl 0485.65036
Rump, S. M.
14
1982
E-methods for fixed point equations f(x)=x. Zbl 0474.65039
Kaucher, E.; Rump, S. M.
7
1982
Kleine Fehlerschranken bei Matrixproblemen. Zbl 0437.65036
Rump, Siegfried M.
29
1980
Small bounds for the solution of systems of linear equations. Zbl 0419.65023
Rump, S. M.; Kaucher, E.
5
1980
Polynomial minimum root separation. Zbl 0405.12018
Rump, Siegfried M.
12
1979
all top 5

Cited by 788 Authors

51 Rump, Siegfried Michael
27 Nakao, Mitsuhiro T.
27 Oishi, Shin’ichi
23 Miyajima, Shinya
23 Ogita, Takeshi
20 Hladík, Milan
20 Lessard, Jean-Philippe
16 Wei, Yimin
15 Watanabe, Yoshitaka
13 James, J. D. Mireles
11 Ozaki, Katsuhisa
10 Diao, Huaian
10 Graillat, Stef
9 Ryoo, Cheon Seoung
8 Castelli, Roberto
8 Kinoshita, Takehiko
8 van den Berg, Jan Bouwe
7 Bünger, Florian
7 Cheng, Lizhi
7 Goldsztejn, Alexandre
7 Hashemi, Behnam
7 Jiang, Hao
7 Mayer, Günter
7 Minamoto, Teruya
7 Nagatou, Kaori
7 Petković, Miodrag S.
7 Plum, Michael
7 Popova, Evgenija D.
7 Sharyĭ, Sergeĭ Petrovich
7 Skalna, Iwona
7 Yamamoto, Nobito
6 Frommer, Andreas
6 Jansson, Christian
6 Jeannerod, Claude-Pierre
6 Kimura, Takuma
6 Liu, Xuefeng
6 Mireles-James, Jason D.
5 Alefeld, Götz E.
5 Dehghan Takht Fooladi, Mehdi
5 Higham, Nicholas J.
5 Kearfott, Baker
5 Kolev, Lubomir V.
5 Krämer, Walter
5 Li, Hanyu
5 Melquiond, Guillaume
5 Muller, Jean-Michel
5 Neumaier, Arnold
5 Pan, Victor Yakovlevich
5 Pham Huu Anh Ngoc
5 Rohn, Jiri
5 Takayasu, Akitoshi
5 Tanaka, Kazuaki
4 Breden, Maxime
4 Chen, Xiaojun
4 Csendes, Tibor
4 Domes, Ferenc
4 Griewank, Andreas
4 Kressner, Daniel
4 Li, Zhe
4 Mizuguchi, Makoto
4 Mullen, Robert L.
4 Noschese, Silvia
4 Qian, Guoliang
4 Tsigaridas, Elias P.
3 Aishima, Kensuke
3 Barrio, Roberto
3 Boldo, Sylvie
3 Capinski, Maciej J.
3 Černý, Michal
3 Dehghani-Madiseh, Marzieh
3 Dobner, Hans-Jürgen
3 Du, Peibing
3 Eichfelder, Gabriele
3 Fernandes, Luiz Gustavo
3 Franek, Peter
3 Gameiro, Marcio F.
3 Hashimoto, Kouji
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 Lange, Marko
3 Liao, Xiangke
3 Louvet, Nicolas
3 Mary, Theo A.
3 Miyaji, Tomoyuki
3 Muhanna, Rafi L.
3 Murphy, Brian J.
3 Naito, Toshiki
3 Nataraj, Paluri S. V.
3 Okamoto, Hisashi
3 Peña, Javier F.
3 Qiao, Sanzheng
3 Radons, Manuel
3 Reinhardt, Christian
3 Rosholt, Rhys Eric
3 Roux, Pierre
...and 688 more Authors
all top 5

Cited in 165 Serials

82 Journal of Computational and Applied Mathematics
56 Linear Algebra and its Applications
37 Computing
30 Applied Mathematics and Computation
29 Japan Journal of Industrial and Applied Mathematics
21 Numerical Algorithms
18 BIT
17 Reliable Computing
16 Computers & Mathematics with Applications
13 Journal of Differential Equations
12 Journal of Global Optimization
10 Numerische Mathematik
9 Mathematics of Computation
9 Theoretical Computer Science
9 Numerical Linear Algebra with Applications
8 Applied Numerical Mathematics
8 Journal of Symbolic Computation
8 SIAM Journal on Applied Dynamical Systems
7 Automatica
7 SIAM Journal on Matrix Analysis and Applications
7 SIAM Journal on Scientific Computing
6 Journal of Mathematical Analysis and Applications
6 Calcolo
4 ACM Transactions on Mathematical Software
4 Journal of Automated Reasoning
4 International Journal of Computer Mathematics
4 Indagationes Mathematicae. New Series
4 ELA. The Electronic Journal of Linear Algebra
4 Optimization Methods & Software
4 Soft Computing
4 Mathematics in Computer Science
3 Journal of Computational Physics
3 Mathematics and Computers in Simulation
3 Applied Mathematics Letters
3 Applied Mathematical Modelling
3 Mathematical Programming. Series A. Series B
3 Celestial Mechanics and Dynamical Astronomy
3 Applicable Algebra in Engineering, Communication and Computing
3 Formal Methods in System Design
3 Computational and Applied Mathematics
3 Advances in Computational Mathematics
3 Engineering Analysis with Boundary Elements
3 Chaos
3 Foundations of Computational Mathematics
3 Optimization Letters
3 Journal of Computational Dynamics
2 Artificial Intelligence
2 Computer Methods in Applied Mechanics and Engineering
2 Journal of the Franklin Institute
2 Linear and Multilinear Algebra
2 Nonlinearity
2 Information Sciences
2 International Journal for Numerical Methods in Engineering
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Numerical Functional Analysis and Optimization
2 SIAM Journal on Numerical Analysis
2 Systems & Control Letters
2 Acta Applicandae Mathematicae
2 Physica D
2 Discrete & Computational Geometry
2 Information and Computation
2 Computers & Operations Research
2 Applications of Mathematics
2 Computational Statistics
2 European Journal of Operational Research
2 Journal of Dynamics and Differential Equations
2 International Journal of Robust and Nonlinear Control
2 Journal of Nonlinear Science
2 ETNA. Electronic Transactions on Numerical Analysis
2 Discrete and Continuous Dynamical Systems
2 Constraints
2 Journal of Inequalities and Applications
2 Methodology and Computing in Applied Probability
2 Journal of Applied Mathematics
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 Information Processing Letters
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Journal of Engineering Mathematics
1 Acta Mathematica
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
1 Revista de la Unión Matemática Argentina
1 Transactions of the American Mathematical Society
1 Advances in Applied Mathematics
1 Zeitschrift für Analysis und ihre Anwendungen
1 Operations Research Letters
1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik
1 Japan Journal of Applied Mathematics
1 Journal of Complexity
...and 65 more Serials
all top 5

Cited in 46 Fields

509 Numerical analysis (65-XX)
137 Linear and multilinear algebra; matrix theory (15-XX)
74 Operations research, mathematical programming (90-XX)
70 Partial differential equations (35-XX)
59 Computer science (68-XX)
47 Ordinary differential equations (34-XX)
37 Dynamical systems and ergodic theory (37-XX)
27 Systems theory; control (93-XX)
25 Operator theory (47-XX)
16 Functions of a complex variable (30-XX)
16 Fluid mechanics (76-XX)
14 Calculus of variations and optimal control; optimization (49-XX)
14 Mechanics of deformable solids (74-XX)
13 Field theory and polynomials (12-XX)
13 Real functions (26-XX)
11 Approximations and expansions (41-XX)
11 Mechanics of particles and systems (70-XX)
9 Commutative algebra (13-XX)
9 Probability theory and stochastic processes (60-XX)
9 Statistics (62-XX)
8 Number theory (11-XX)
7 Information and communication theory, circuits (94-XX)
6 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
6 Biology and other natural sciences (92-XX)
5 Difference and functional equations (39-XX)
5 Global analysis, analysis on manifolds (58-XX)
4 Mathematical logic and foundations (03-XX)
4 Combinatorics (05-XX)
4 Algebraic geometry (14-XX)
4 Functional analysis (46-XX)
3 Measure and integration (28-XX)
3 Special functions (33-XX)
3 Integral equations (45-XX)
3 Optics, electromagnetic theory (78-XX)
2 Harmonic analysis on Euclidean spaces (42-XX)
2 Geometry (51-XX)
2 Convex and discrete geometry (52-XX)
2 Algebraic topology (55-XX)
2 Statistical mechanics, structure of matter (82-XX)
1 General algebraic systems (08-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Differential geometry (53-XX)
1 General topology (54-XX)
1 Manifolds and cell complexes (57-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Quantum theory (81-XX)

Citations by Year