| Publication | Date of Publication | Type |
|---|
| Fast and accurate computation of the Euclidean norm of a vector | 2023-10-13 | Paper |
| Fast computation of error bounds for all eigenpairs of a Hermitian and all singular pairs of a rectangular matrix with emphasis on eigen- and singular value clusters | 2023-07-21 | Paper |
| Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-\(p\) base \(\beta\) | 2023-05-03 | Paper |
| When does ‖f(A)‖ = f(‖A‖) hold true? | 2023-04-25 | Paper |
| Verified Error Bounds for All Eigenvalues and Eigenvectors of a Matrix | 2022-12-19 | Paper |
| Entrywise lower and upper bounds for the Perron vector | 2022-09-28 | Paper |
| Convergence results for some piecewise linear solvers | 2022-06-10 | Paper |
| On norms of principal submatrices | 2021-04-24 | Paper |
| Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin's \(\sin (\theta)\) theorem | 2021-03-31 | Paper |
| Addendum to: ``On recurrences converging to the wrong limit in finite precision and some new examples | 2021-01-18 | Paper |
| Faithfully Rounded Floating-point Computations | 2020-11-10 | Paper |
| On recurrences converging to the wrong limit in finite precision and some new examples | 2020-10-06 | Paper |
| Verified bounds for the determinant of real or complex point or interval matrices | 2020-02-18 | Paper |
| Modified error bounds for approximate solutions of dense linear systems | 2020-02-05 | Paper |
| Lower bounds for the smallest singular value of certain Toeplitz-like triangular matrices with linearly increasing diagonal entries | 2019-10-28 | Paper |
| Complex disk products and Cartesian ovals | 2019-10-17 | Paper |
| The determinant of a complex matrix and Gershgorin circles | 2019-08-28 | Paper |
| Addendum to: ``Estimates of the determinant of a perturbed identity matrix | 2019-03-26 | Paper |
| Bounds for the determinant by Gershgorin circles | 2019-01-24 | Paper |
| Estimates of the determinant of a perturbed identity matrix | 2018-10-11 | Paper |
| Mathematically rigorous global optimization in floating-point arithmetic | 2018-10-09 | Paper |
| Sharp estimates for perturbation errors in summations | 2018-09-20 | Paper |
| IEEE754 Precision- k base-β Arithmetic Inherited by Precision- m Base-β Arithmetic for k < m | 2018-07-20 | Paper |
| On relative errors of floating-point operations: Optimal bounds and applications | 2018-01-12 | Paper |
| Error estimates for the summation of real numbers with application to floating-point summation | 2017-10-24 | Paper |
| Sign controlled solvers for the absolute value equation with an application to support vector machines | 2017-07-28 | Paper |
| Yet more elementary proofs that the determinant of a symplectic matrix is 1 | 2016-12-29 | Paper |
| Floating-point arithmetic on the test bench. How are verified numerical solutions calculated? | 2016-11-02 | Paper |
| Simple floating-point filters for the two-dimensional orientation problem | 2016-06-10 | Paper |
| Improved error bounds for floating-point products and Horner's scheme | 2016-05-19 | Paper |
| On the definition of unit roundoff | 2016-05-19 | Paper |
| The Componentwise Structured and Unstructured Backward Errors Can be Arbitrarily Far Apart | 2015-06-09 | Paper |
| Improved Backward Error Bounds for LU and Cholesky Factorizations | 2014-10-15 | Paper |
| Improved componentwise verified error bounds for least squares problems and underdetermined linear systems | 2014-07-03 | Paper |
| Improved Error Bounds for Inner Products in Floating-Point Arithmetic | 2013-09-26 | Paper |
| Accurate solution of dense linear systems I: Algorithms in rounding to nearest | 2013-01-21 | Paper |
| Accurate solution of dense linear systems. II: Algorithms using directed rounding | 2013-01-21 | Paper |
| Interval arithmetic over finitely many endpoints | 2012-12-20 | Paper |
| Fast interval matrix multiplication | 2012-09-24 | Paper |
| Verified Bounds for Least Squares Problems and Underdetermined Linear Systems | 2012-08-23 | Paper |
| Verification methods: Rigorous results using floating-point arithmetic | 2012-06-11 | Paper |
| Fast algorithms for floating-point interval matrix multiplication | 2012-04-24 | Paper |
| Error estimation of floating-point summation and dot product | 2012-03-23 | Paper |
| Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications | 2012-02-13 | Paper |
| Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse | 2011-08-02 | Paper |
| Ultimately Fast Accurate Summation | 2010-10-19 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3162307 | 2010-10-19 | Paper |
| Verified error bounds for multiple roots of systems of nonlinear equations | 2010-09-16 | Paper |
| Accurate and Reliable Computing in Floating-Point Arithmetic | 2010-09-14 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3583363 | 2010-08-27 | Paper |
| Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest | 2010-05-06 | Paper |
| Accurate Floating-Point Summation Part I: Faithful Rounding | 2010-03-10 | Paper |
| Adaptive and efficient algorithm for 2D orientation problem | 2010-02-25 | Paper |
| Inversion of extremely ill-conditioned matrices in floating-point | 2010-02-25 | Paper |
| Iterative refinement for ill-conditioned linear systems | 2010-02-25 | Paper |
| Computing predecessor and successor in rounding to nearest | 2009-07-24 | Paper |
| Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices | 2007-07-17 | Paper |
| Super-fast validated solution of linear systems | 2007-02-02 | Paper |
| A method of obtaining verified solutions for linear systems suited for Java | 2007-02-02 | Paper |
| Towards optimal use of multi-precision arithmetic: a remark | 2006-09-14 | Paper |
| Verification of positive definiteness | 2006-09-12 | Paper |
| Eigenvalues, pseudospectrum and structured perturbations | 2006-03-22 | Paper |
| Accurate Sum and Dot Product | 2005-09-22 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4656576 | 2005-03-11 | Paper |
| On eigenvector bounds | 2004-03-15 | Paper |
| Structured Perturbations Part I: Normwise Distances | 2004-01-18 | Paper |
| Structured Perturbations Part II: Componentwise Distances | 2004-01-18 | Paper |
| Ten methods to bound multiple roots of polynomials | 2003-08-07 | Paper |
| Variational characterizations of the sign-real and the sign-complex spectral radius | 2003-07-06 | Paper |
| Optimal scaling for p-norms and componentwise distance to singularity | 2003-05-14 | Paper |
| On \(P\)-matrices | 2003-05-04 | Paper |
| Perron-Frobenius theory for complex matrices | 2003-05-04 | Paper |
| Conservatism of the circle criterion-solution of a problem posed by A. Megretski | 2002-07-21 | Paper |
| Fast verification of solutions of matrix equations | 2002-05-21 | Paper |
| Rigorous and portable standard functions | 2002-02-19 | Paper |
| Ill-conditionedness need not be componentwise near to ill-posedness for least squares problems | 2001-10-24 | Paper |
| https://portal.mardi4nfdi.de/entity/Q2738493 | 2001-08-30 | Paper |
| Computational error bounds for multiple or nearly multiple eigenvalues | 2001-07-03 | Paper |
| Self-validating methods | 2001-04-16 | Paper |
| Structured perturbations and symmetric matrices | 2000-11-21 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4945762 | 2000-09-05 | Paper |
| The sign-real spectral radius and cycle products | 2000-08-28 | Paper |
| Fast and parallel interval arithmetic | 2000-08-21 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4949347 | 2000-05-08 | Paper |
| A note on epsilon-inflation | 1999-09-09 | Paper |
| Ill-Conditioned Matrices Are Componentwise Near to Singularity | 1999-06-27 | Paper |
| Theorems of Perron-Frobenius type for matrices without sign restrictions | 1998-11-26 | Paper |
| Intervals and the origins of calculus | 1998-06-08 | Paper |
| Almost Sharp Bounds for the Componentwise Distance to the Nearest Singular Matrix | 1997-12-10 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4358188 | 1997-11-12 | Paper |
| Inclusion of zeros of nowhere differentiable \(n\)-dimensional functions | 1997-08-07 | Paper |
| Bounds for the Componentwise Distance to the Nearest Singular Matrix | 1997-07-28 | Paper |
| Verified solution of large systems and global optimization problems | 1997-07-13 | Paper |
| Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems | 1997-05-25 | Paper |
| Expansion and estimation of the range of nonlinear functions | 1996-12-03 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4885359 | 1996-10-27 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4868545 | 1996-06-03 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4284596 | 1996-05-21 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4847626 | 1996-02-26 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4849573 | 1995-10-04 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4321536 | 1995-05-28 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4310321 | 1994-11-10 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4308281 | 1994-10-26 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4295151 | 1994-07-04 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4026744 | 1993-02-21 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4006782 | 1992-09-27 | Paper |
| On the solution of interval linear systems | 1992-06-28 | Paper |
| A Class of Arbitrarily Ill Conditioned Floating-Point Matrices | 1992-06-26 | Paper |
| Rigorous solution of linear programming problems with uncertain data | 1992-06-25 | Paper |
| Estimation of the sensitivity of linear and nonlinear algebraic problems | 1992-06-25 | Paper |
| Rigorous Sensitivity Analysis for Systems of Linear and Nonlinear Equations | 1990-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3486360 | 1990-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4732105 | 1989-01-01 | Paper |
| Guaranteed inclusions for the complex generalized eigenproblem | 1989-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4203694 | 1989-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3813151 | 1988-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3813269 | 1988-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3816912 | 1988-01-01 | Paper |
| FORTRAN-SC. A study of a FORTRAN extension for engineering/scientific computation with access to ACRITH | 1987-01-01 | Paper |
| Solution of linear systems with verified accuracy | 1987-01-01 | Paper |
| Sichere Ergebnisse auf Rechenanlagen | 1986-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3750040 | 1986-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3750041 | 1986-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3340041 | 1984-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3036594 | 1983-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3666142 | 1983-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3730925 | 1983-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3730926 | 1983-01-01 | Paper |
| E-methods for fixed point equations f(x)=x | 1982-01-01 | Paper |
| Solving nonlinear systems with least significant bit accuracy | 1982-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3666141 | 1982-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3947055 | 1981-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3947056 | 1981-01-01 | Paper |
| Generalized iteration methods for bounds of the solution of fixed point operator-equations | 1980-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3853054 | 1980-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3862950 | 1980-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3868724 | 1980-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3878653 | 1980-01-01 | Paper |
| Polynomial Minimum Root Separation | 1979-01-01 | Paper |
