Minimum Rank Solutions to the Matrix Approximation Problems in the Spectral Norm

DOI10.1137/110851134zbMath1260.15024OpenAlexW2042683239MaRDI QIDQ4902928

Musheng Wei, Dongmei Shen

Publication date: 18 January 2013

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

Full work available at URL: https://doi.org/10.1137/110851134

zbMATH Keywords

SVDminimum rankmatrix approximationnorm-preserving dilationsR-SVD

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Linear programming (90C05) Matrix equations and identities (15A24) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) General systems (93A10)

Related Items (12)

The minimal rank of \(A - BX\) with respect to Hermitian matrix ⋮ The minimal rank of matrix expressions with respect to Hermitian matrix-revised ⋮ On least squares solutions subject to a rank restriction ⋮ Minimum rank positive semidefinite solution to the matrix approximation problem in the spectral norm ⋮ Norm-preserving dilation theorems for a block positive semidefinite (definite) matrix ⋮ Rank constrained matrix best approximation problem ⋮ On extremal ranks and least squares solutions subject to a rank restriction ⋮ Rank constrained matrix best approximation problem with respect to (skew) Hermitian matrices ⋮ Minimum rank Hermitian solution to the matrix approximation problem in the spectral norm and its application ⋮ Least squares solutions to the rank-constrained matrix approximation problem in the Frobenius norm ⋮ G-frame operator distance problems ⋮ Minimum rank (skew) Hermitian solutions to the matrix approximation problem in the spectral norm

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