Structured condition numbers and statistical condition estimation for the \(LDU\) factorization

DOI10.1007/s11766-020-3659-4zbMath1474.65104OpenAlexW3084804294MaRDI QIDQ2221519

Aamir Farooq, Mahvish Samar, Chun-Lai Mu

Publication date: 2 February 2021

Published in: Applied Mathematics. Series B (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11766-020-3659-4

zbMATH Keywords

\(LDU\) factorizationstructured condition numbernormwise condition numbercomponentwise condition numbermixed condition number

Mathematics Subject Classification ID

Factorization of matrices (15A23) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (2)

Condition numbers for a linear function of the solution to the constrained and weighted least squares problem and their statistical estimation ⋮ Refined rigorous perturbation bounds for the SR decomposition

Cites Work

• Condition numbers for the nonlinear matrix equation and their statistical estimation
• Perturbation theory for the LDU factorization and accurate computations for diagonally dominant matrices
• Sensitivity analyses for factorizations of sparse or structured matrices
• LDU factorization results for bi-infinite and semi-infinite scalar and block Toeplitz matrices
• On the sensitivity of the LU factorization
• Structured condition numbers for some matrix factorizations of structured matrices
• Partial condition number for the equality constrained linear least squares problem
• Probabilistic upper bounds for the matrix two-norm
• Numerical properties of shifted tridiagonal LU factorizations
• Stability and sensitivity of tridiagonal LU factorization without pivoting
• A New Perturbation Bound for the LDU Factorization of Diagonally Dominant Matrices
• Mixed, Componentwise, and Structured Condition Numbers
• Perturbation analysis for the periodic generalized coupled Sylvester equation
• Small-Sample Statistical Condition Estimates for General Matrix Functions
• Perturbation Analyses for the QR Factorization
• A Theory of Condition
• New perturbation analyses for the Cholesky factorization
• On condition numbers for the canonical generalized polar decompostion of real matrices
• Mixed and componentwise condition numbers for matrix decompositions
• Mixed and componentwise condition numbers for matrix decompositions
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