Small singular values can increase in lower precision

DOI10.1137/23m1557209zbMATH Open1545.65153MaRDI QIDQ6592219

Petros Drineas, Christos Boutsikas, Ilse C. F. Ipsen

Publication date: 24 August 2024

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

perturbation theoryeigenvaluessingular valuesLoewner partial orderingarithmetic precisionreal symmetric positive semi-definite matrices

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18)

Cites Work

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• A note on a lower bound for the smallest singular value
• A Gershgorin-type lower bound for the smallest singular value
• A second order perturbation expansion for small singular values
• Inversion of extremely ill-conditioned matrices in floating-point
• Perturbation of the SVD in the presence of small singular values
• Estimation of \(\| A ^{-1} \|_\infty \) and the smallest singular value
• A lower bound for the smallest singular value
• A lower bound for the smallest singular value of a matrix
• Further lower bounds for the smallest singular value
• Schur complement-based infinity norm bounds for the inverse of SDD matrices
• On some lower bounds for smallest singular value of matrices
• Schur complement-based infinity norm bounds for the inverse of \(DSDD\) matrices
• A lower bound for the smallest singular value
• Two new lower bounds for the smallest singular value
• Calculating the Singular Values and Pseudo-Inverse of a Matrix
• Lower bounds for the smallest singular values of generalized asymptotic diagonal dominant matrices

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