Geometrical properties of the Frobenius condition number for positive definite matrices

DOI10.1016/j.laa.2008.06.006zbMath1153.15009OpenAlexW1973401146MaRDI QIDQ947673

Jean-Paul Chehab, Marcos Raydan

Publication date: 6 October 2008

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.06.006

zbMATH Keywords

numerical experimentscondition numberFrobenius normcones of matricesFrobenius inner product

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45) Quadratic and bilinear forms, inner products (15A63) Conditioning of matrices (15A12)

Related Items

Geometrical inverse matrix approximation for least-squares problems and acceleration strategies ⋮ Geometrical and spectral properties of the orthogonal projections of the identity ⋮ On the Frobenius condition number of positive definite matrices ⋮ On the geometrical structure of symmetric matrices ⋮ Geometrical inverse preconditioning for symmetric positive definite matrices ⋮ Recovering a perturbation of a matrix polynomial from a perturbation of its first companion linearization

Cites Work

• A best upper bound for the 2-norm condition number of a matrix
• More estimates for eigenvalues and singular values
• Eigenvalue estimates for symmetric matrices
• Bounds for eigenvalues using traces
• On the cone of positive semidefinite matrices
• Preconditioning techniques for large linear systems: A survey
• New bounds for the extreme values of a finite sample of real numbers
• An estimator for the diagonal of a matrix
• Some large-scale matrix computation problems
• On pairs of vectors achieving the maximal angle of a convex cone
• Measuring the degree of pointedness of a closed convex cone: a metric approach
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