Ill-Conditioned Matrices Are Componentwise Near to Singularity

DOI10.1137/S0036144598323216zbMath0923.15003MaRDI QIDQ4255826

Siegfried Michael Rump

Publication date: 27 June 1999

Published in: SIAM Review (Search for Journal in Brave)

zbMATH Keywords

sign-real spectral radiusill conditioningcomponentwise distancenearest singular matrix

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12)

Related Items (14)

Accurate determinants of some classes of matrices ⋮ Generalized eigenvalue for even order tensors via Einstein product and its applications in multilinear control systems ⋮ On sign-real spectral radii and sign-real expansive matrices ⋮ A characterization of the distance to infeasibility under block-structured perturbations ⋮ A sharp version of Bauer-Fike's theorem ⋮ Composite norms and perfect conditioning ⋮ A numerical algorithm for zero counting. III: Randomization and condition ⋮ Some classes of nonsingular matrices with applications to localize the real eigenvalues of real matrices ⋮ On the block-structured distance to non-surjectivity of sublinear mappings ⋮ Conic systems and sublinear mappings: equivalent approaches. ⋮ Unnamed Item ⋮ Convergence of Rump’s method for computing the Moore-Penrose inverse ⋮ Componentwise pseudospectrum of a matrix ⋮ Perron-Frobenius theory for complex matrices

Uses Software

• mctoolbox

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