Perturbation of the SVD in the presence of small singular values

DOI10.1016/j.laa.2006.04.013zbMath1111.65037OpenAlexW2018670063MaRDI QIDQ854854

Michael Stewart

Publication date: 7 December 2006

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

Full work available at URL: https://doi.org/10.1016/j.laa.2006.04.013

zbMATH Keywords

singular values decompositionOverdetermined SystemsPerturbation TheoryPseudoinversesSingular subspace

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20)

Related Items (9)

A Schatten-\(q\) low-rank matrix perturbation analysis via perturbation projection error bound ⋮ An interval perturbation method for singular value decomposition (SVD) with unknown-but-bounded (UBB) parameters ⋮ Numerical Rank Deficiency in Matrix Products ⋮ Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics ⋮ Unnamed Item ⋮ A locally optimal rank revealing product decomposition ⋮ Perturbation expansions and error bounds for the truncated singular value decomposition ⋮ Condition number of singular value: zero-structured and patterned case ⋮ Unnamed Item

Cites Work

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• A second order perturbation expansion for small singular values
• Relative Perturbation Theory: II. Eigenspace and Singular Subspace Variations
• A Second-Order Perturbation Expansion for the SVD
• The Rotation of Eigenvectors by a Perturbation. III
• Perturbation bounds in connection with singular value decomposition

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