Siegfried M. Rump
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Siegfried M. Rumpmathematics Degrees
Mathematics
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Applied Mathematics
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Measure Theory
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Mathematics
Siegfried M. Rump's Degrees
- PhD Mathematics University of Hamburg
Why Is Siegfried M. Rump Influential?
(Suggest an Edit or Addition)Siegfried M. Rump's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- INTLAB - INTerval LABoratory (1998) (1208)
- Accurate Sum and Dot Product (2005) (427)
- Verification methods: rigorous results using floating-point arithmetic (2010) (308)
- Verification methods for dense and sparse systems of equations (1994) (234)
- Solving Algebraic Problems with High Accuracy (1983) (221)
- Accurate Floating-Point Summation Part I: Faithful Rounding (2008) (191)
- Fast and Parallel Interval Arithmetic (1999) (162)
- Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest (2008) (95)
- Ultimately Fast Accurate Summation (2009) (84)
- Structured Perturbations Part I: Normwise Distances (2003) (71)
- Computational error bounds for multiple or nearly multiple eigenvalues (2001) (70)
- Verification of Positive Definiteness (2006) (67)
- Fast verification of solutions of matrix equations (2002) (66)
- Rigorous sensitivity analysis for systems of linear and nonlinear equations (1990) (58)
- EIGENVALUES, PSEUDOSPECTRUM AND STRUCTURED PERTURBATIONS (2006) (57)
- On the solution of interval linear systems (1991) (57)
- Algorithms for verified inclusions—theory and practice (1988) (56)
- Ten methods to bound multiple roots of polynomials (2003) (53)
- Improved Error Bounds for Inner Products in Floating-Point Arithmetic (2013) (52)
- Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse (2011) (50)
- Inversion of extremely Ill-conditioned matrices in floating-point (2009) (47)
- Error estimation of floating-point summation and dot product (2012) (46)
- Validated solution of large linear systems (1993) (46)
- Implementation and improvements of affine arithmetic (2015) (44)
- Verified error bounds for multiple roots of systems of nonlinear equations (2010) (43)
- Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications (2011) (42)
- THEOREMS OF PERRON-FROBENIUS TYPE FOR MATRICES WITHOUT SIGN RESTRICTIONS (1997) (42)
- Structured Perturbations Part II: Componentwise Distances (2003) (41)
- Self-validating methods (2001) (40)
- Expansion and estimation of the range of nonlinear functions (1996) (39)
- A Note on Epsilon-Inflation (1998) (39)
- Rigorous solution of linear programming problems with uncertain data (1991) (39)
- Ill-Conditioned Matrices Are Componentwise Near to Singularity (1999) (38)
- On relative errors of floating-point operations: Optimal bounds and applications (2017) (37)
- Perron–Frobenius theory for complex matrices (2003) (37)
- Symbolic Algebraic Methods and Verification Methods (2001) (35)
- Bounds for the Componentwise Distance to the Nearest Singular Matrix (1997) (34)
- Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices (2007) (30)
- New Results on Verified Inclusions (1985) (30)
- A parallel algorithm for accurate dot product (2008) (30)
- A class of arbitrarily ill conditioned floating-point matrices (1991) (30)
- Polynomial minimum root separation (1979) (27)
- Guaranteed inclusions for the complex generalized eigenproblem (1989) (24)
- 10. Computer-Assisted Proofs and Self-Validating Methods (2005) (24)
- Super-fast validated solution of linear systems (2007) (22)
- Approximate inverses of almost singular matrices still contain useful information (1990) (22)
- On Eigenvector Bounds (2003) (21)
- Fast Verification for All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problems (2010) (21)
- Small Bounds for the Solution of Systems of Linear Equations (1980) (21)
- Improved Backward Error Bounds for LU and Cholesky Factorizations (2014) (21)
- Fast high precision summation (2010) (21)
- On P-matrices (2003) (21)
- Optimal scaling for p‐norms and componentwise distance to singularity (2003) (21)
- Computing predecessor and successor in rounding to nearest (2009) (20)
- Almost Sharp Bounds for the Componentwise Distance to the Nearest Singular Matrix (1997) (18)
- Accurate solution of dense linear systems, Part II: Algorithms using directed rounding (2013) (18)
- Algebraic Computation, Numerical Computation and Verified Inclusions (1988) (17)
- Fast interval matrix multiplication (2012) (17)
- Solution of linear and nonlinear algebraic problems with sharp, guaranteed bounds (1984) (17)
- Verified Bounds for Least Squares Problems and Underdetermined Linear Systems (2012) (16)
- On the sign of a real algebraic number (1976) (15)
- Accurate solution of dense linear systems, part I: Algorithms in rounding to nearest (2013) (15)
- ACCURATE FLOATING-POINT SUMMATION (2005) (15)
- Towards Optimal Use of Multi-Precision Arithmetic: A Remark (2006) (14)
- The Ratio Between the Toeplitz and the Unstructured Condition Number (2010) (14)
- Fast algorithms for floating-point interval matrix multiplication (2012) (13)
- Rigorous and Portable Standard Functions (2001) (13)
- Numerical Verification Method for Arbitrarily Ill-conditioned Linear Systems (2005) (12)
- A method of obtaining verified solutions for linear systems suited for Java (2007) (11)
- VERIFIED SOLUTIONS OF LINEAR SYSTEMS WITHOUT DIRECTED ROUNDING (2005) (11)
- Estimation of the Sensitivity of Linear and Nonlinear Algebraic Problems (1991) (11)
- EVALUATION OF HEDGE EFFECTIVENESS TESTS (2005) (11)
- PASCAL-SC: A PASCAL for Contemporary Scientific Computation (1981) (10)
- STRUCTURED PERTURBATIONS AND SYMMETRIC MATRICES (1998) (9)
- How reliable are results of computers (1983) (9)
- Improved componentwise verified error bounds for least squares problems and underdetermined linear systems (2014) (9)
- IEEE754 Precision-k base-β Arithmetic Inherited by Precision-m Base-β Arithmetic for k < m (2016) (8)
- ACRITH - High Accuracy Arithmetic Subroutine Library (1985) (8)
- Sharp estimates for perturbation errors in summations (2018) (8)
- Special Issue on Validated Numerical Methods and Computer Algebra. Foreword of the Guest Editors (1997) (8)
- Adaptive and efficient algorithm for 2D orientation problem (2009) (8)
- Improved error bounds for floating-point products and Horner’s scheme (2016) (8)
- Ill-Conditionedness Need not be Componentwise Near to Ill-Posedness for Least Squares Problems (1999) (8)
- Error estimates for the summation of real numbers with application to floating-point summation (2017) (7)
- THE SIGN-REAL SPECTRAL RADIUS AND CYCLE PRODUCTS (1998) (7)
- Verified solution of large systems and global optimization problems (1995) (7)
- Intervals and the Origins of Calculus (1998) (7)
- FORTRAN-SC a study of a FORTRAN extension for engineering/scientific computation with access to ACRITH (1987) (7)
- Accurate Matrix Multiplication by using Level 3 BLAS Operation (2008) (7)
- Estimates of the determinant of a perturbed identity matrix (2018) (6)
- Interval arithmetic with fixed rounding mode (2016) (6)
- Faithfully Rounded Floating-point Computations (2020) (6)
- On the generation of very ill-conditioned integer matrices (2011) (6)
- Iterative refinement for ill-conditioned linear systems (2009) (6)
- Simple floating-point filters for the two-dimensional orientation problem (2016) (6)
- Solving nonlinear systems with least significant bit accuracy (1982) (6)
- E-methods for fixed point equations f(x)=x (1982) (6)
- ACRITH: High-Accuracy Arithmetic an advanced tool for numerical computation (1985) (6)
- Generalization of error-free transformation for matrix multiplication and its application (2013) (6)
- Rigorous results in electronic structure calculations (2016) (6)
- Inclusion of Zeros of Nowhere Differentiable n-Dimensional Functions (1997) (5)
- Improved error bounds for linear systems with H-matrices (2015) (5)
- Conservatism of the circle criterion-solution of a problem posed by A. Megretski (2001) (5)
- Solution of linear systems with verified accuracy (1987) (5)
- Software Engineering im Scientific Computing (1996) (5)
- Yet more elementary proofs that the determinant of a symplectic matrix is 1 (2017) (5)
- A Method for the Generation of a Class of Ill-conditioned Matrices (2008) (5)
- Global optimization : a model problem (2007) (5)
- On the definition of unit roundoff (2016) (5)
- Iterative Refinement for Ill-conditioned Linear Equations. (2008) (5)
- Case Studies for Augmented Floating-Point (1985) (5)
- Verified Solution of Large Linear and Nonlinear Systems (1999) (5)
- Interval arithmetic over finitely many endpoints (2012) (4)
- Verified computation of a disc containing exactly k roots of a univariate nonlinear function (2010) (4)
- Verified sharp bounds for the real gamma function over the entire floating-point range (2014) (4)
- Numerical Verification Method for Dense Linear Systems with Arbitrarily Ill-conditioned Matrices (2005) (4)
- Real root isolation for algebraic polynomials (1977) (4)
- Convergence Properties of Iterations Using Sets (1991) (4)
- High precision evaluation of nonlinear functions (2005) (4)
- Least significant bit evaluation of arithmetic expressions in single-precision (1983) (4)
- Bounds for the determinant by Gershgorin circles (2019) (3)
- Accurate and Reliable Computing in Floating-Point Arithmetic (2010) (3)
- Proposal for Arithmetic Specification in FORTRAN 8x (1982) (3)
- VARIATIONAL CHARACTERIZATIONS OF THE SIGN-REAL AND THE SIGN-COMPLEX SPECTRAL RADIUS ∗ (2002) (3)
- Mathematically rigorous global optimization in floating-point arithmetic (2018) (3)
- Computer demonstration packages for standard problems of numerical mathematics (1983) (3)
- Algebraic and Numerical Algorithms and Computer-assisted Proofs, 25.-30. September 2005 (2006) (3)
- A model problem for global optimization (2011) (3)
- Error Bounds for Computer Arithmetics (2019) (3)
- Generalized iteration methods for bounds of the solution of fixed point operator-equations (1980) (3)
- Verification methods: Rigorous . . . (2010) (3)
- Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems (1996) (3)
- The Componentwise Structured and Unstructured Backward Errors Can be Arbitrarily Far Apart (2015) (3)
- A consideration on the condition number of extremely ill-conditioned matrices (2013) (2)
- Introduction to ACRITH - Accurate Scientific Algorithms (1987) (2)
- The determinant of a complex matrix and Gershgorin circles (2019) (2)
- Error bounds for extremely ill-conditioned problems (2006) (2)
- Verified Bounds for the p-Norm Condition Number (2014) (2)
- 05391 Executive Summary - Numerical and Algebraic Algorithms and Computer-assisted Proofs (2005) (2)
- Inclusion methods for real and complex functions in one variable (1995) (2)
- Positive entries of stable matrices (2005) (2)
- Lower Bounds for the Smallest Singular Value of Certain Toeplitz-like Triangular Matrices with Linearly Increasing Diagonal Entries (2019) (1)
- Lineare Probleme (1989) (1)
- MATRIX PASCAL (1983) (1)
- PREDECESSOR AND SUCCESSOR IN ROUNDING TO NEAREST (2006) (1)
- Verified Solutions of Sparse Linear Systems by LU factorization (2005) (1)
- Sign controlled solvers for the absolute value equation with an application to support vector machines (2017) (1)
- Error estimation of floating-point summation and dot product (2011) (1)
- A consideration on the generation of extremely ill-conditioned matrices (非線形問題) (2013) (1)
- Componentwise Verified Solutions of Linear Systems Suited for Java (2005) (1)
- Accuracy Control and Estimation, Self-Validating Systems and Software Environments for Scientific Computation (1991) (1)
- Special section on recent progress in numerical verification (2011) (1)
- Interval arithmetic on the Cell processor (2008) (1)
- Verified bounds for the determinant of real or complex point or interval matrices (2020) (1)
- Addendum to “Estimates of the determinant of a perturbed identity matrix” [Linear Algebra Appl. 558 (2018) 101–107] (2019) (1)
- Interval operations in rounding to nearest (2007) (1)
- Higher Order Computer Arithmetic (1985) (1)
- Fast Verification Algorithms in MATLAB (2001) (1)
- Improved error bounds for floating-point products and Horner’s scheme (2015) (1)
- Fast Adaptive Algorithm of Geometric Predicates using Floating-Point Arithmetic (2006) (1)
- Addendum to “On recurrences converging to the wrong limit in finite precision and some new examples” (2020) (1)
- On recurrences converging to the wrong limit in finite precision and some new examples (2020) (1)
- Mathematical Aspects of Computer and Information Sciences (2015) (1)
- On Nishi's Conditions for Ω-Property (2003) (1)
- Accurate Matrix Multiplication with Multiple Floating-point Numbers (2007) (1)
- Computable backward error bounds for basic algorithms in linear algebra (2015) (1)
- On the definition of unit roundoff (2015) (0)
- Piecewise smooth system and optimization with piecewise linearization via algorithmic differentiation (NII Shonan Meeting 2018-9) (2018) (0)
- Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin’s $$\sin (\theta )$$ sin ( θ ) theorem (2020) (0)
- ILL-CONDITIONEDNESS NEEDS NOT BE COMPONENTWISE NEAR TO ILL-POSEDNESS FOR LEAST SQUARES PROBLEMS (2005) (0)
- Computer-assisted proofs-tools , methods and applications (2010) (0)
- 05391 Abstracts Collection - Algebraic and Numerical Algorithms and Computer-assisted Proofs (2005) (0)
- 09471 Abstracts Collection - Computer-assisted proofs - tools, methods and applications (2009) (0)
- Reliable Computation and Complexity on the Reals (Dagstuhl Seminar 17481) (2018) (0)
- Convergence results for some piecewise linear solvers (2020) (0)
- Validated Solution of Large Linear Systems 1 (2005) (0)
- Fast veriflcation algorithms in Matlab 1 (2001) (0)
- Rigorous Lower Bounds for the Ground State Energy of Molecules by Employing Necessary N-Representability Conditions. (2020) (0)
- Bounds for the p-Norm Condition Number (2014) (0)
- Introduction: Symbolic Algebraic Methods and Verification Methods (2001) (0)
- Computer-assisted proofs using floating point arithmetic using the new INTLAB (2014) (0)
- 09471 Executive Summary - Computer-assisted proofs - tools, methods and applications (2009) (0)
- More Accurate Computation: Methods and Software [Track Proposal to SAC 2006, Dijon, France.] (2005) (0)
- An Efficient Method Of Applying Accurate Summation Algorithms To 3D Orientation Problem (2007) (0)
- When does ‖f(A)‖ = f(‖A‖) hold true? (2021) (0)
- Generation of ill-conditioned matrices of order n (非線形問題) (2013) (0)
- A Short Note on the Convexity of Interval Matrix-Vector Products ∗ (2016) (0)
- On the Definition of Unit (2014) (0)
- Interval arithmetic over finitely many endpoints (2012) (0)
- BIT 41(3), pp. 540–562, 2001 RIGOROUS AND PORTABLE STANDARD FUNCTIONS (2005) (0)
- Theoretical and Computational Aspects of Matrix Algorithms (Dagstuhl Seminar 03421) (2021) (0)
- Session details: More accurate computation: methods and software (MCMS) (2006) (0)
- Mathematical aspects of computer and information sciences: 6th International Conference, MACIS 2015 Berlin, Germany, November 11–13, 2015 Revised Selected Papers (2016) (0)
- Symbolic, Algebraic and Validated Numerical Computation (Dagstuhl Seminar 9232) (2021) (0)
- Linear systems in matlab with zero residual (2018) (0)
- Improved componentwise verified error bounds for least squares problems and underdetermined linear systems (2013) (0)
- Revised Selected Papers of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences - Volume 9582 (2015) (0)
- Verification methods - mathematically correct results in floating-point, 2nd half (2016) (0)
- COX : C with Operator eXtension (1996) (0)
- Simple floating-point filters for the two-dimensional orientation problem (2015) (0)
- Tight Inclusion for Matrix Multiplication (2008) (0)
- Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-p base β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odd (2023) (0)
- Numerical Methods with Automatic Verification (1985) (0)
- Verified Error Bounds for All Eigenvalues and Eigenvectors of a Matrix (2022) (0)
- Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-p base $$\beta $$ (2023) (0)
- Error estimates for the summation of real numbers with application to floating-point summation (2017) (0)
- Modified error bounds for approximate solutions of dense linear systems (2020) (0)
- Foreword (2021) (0)
- More Accurate Computation: Methods and Software (2006) (0)
- Fast interval matrix multiplication (2011) (0)
- Method and circuit for the addition of floating point numbers. (1986) (0)
- Tight inclusion of matrix multiplication and its portable implementation (2008) (0)
- Arithmetic specification in FORTRAN 8X (1984) (0)
- BIT 39(3), pp. 539–560, 1999 FAST AND PARALLEL INTERVAL ARITHMETIC (2005) (0)
- Fast and Adaptive Algorithm for 2D Orientation Problem (2007) (0)
- Complex Disk Products and Cartesian Ovals (2019) (0)
- Toeplitz structured perturbations (2007) (0)
- AK-1-2 Accurate sum and dot product of floating point vectors and applications (2007) (0)
- Short biography of Shmuel Friedland for his special LAA volume (2009) (0)
- Symbolic-algebraic Methods and Verification Methods - Theory and Applications (Dagstuhl Seminar 99471) (2021) (0)
- BOUNDS FOR THE DETERMINANT BY GERSHGORIN CIRCLES∗ DEDICATED TO ULRICH KULISCH ON THE OCCASION OF HIS 85TH BIRTHDAY (2018) (0)
- Special section on verified numerical computations, Part I (2020) (0)
- Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications (2011) (0)
- Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin’s sin ( (cid:2) ) theorem (2020) (0)
- Computer-assisted proofs-tools , methods and applications Dagstuhl Seminar (2010) (0)
- Error Free Transformation for Matrix Multiplication (2007) (0)
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What Schools Are Affiliated With Siegfried M. Rump?
Siegfried M. Rump is affiliated with the following schools:
