On the sensitivity of the LU factorization

DOI10.1007/BF02510255zbMath0924.65038OpenAlexW2050250211MaRDI QIDQ1272874

Christopher C. Paige, Xiao-Wen Chang

Publication date: 7 March 1999

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02510255

zbMATH Keywords

sensitivitynumerical examplescondition numberspartial pivotingmatrix-vector equation approach\(LU\)-factorizationmatrix equation approach

Mathematics Subject Classification ID

Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

Efficient Solution of a Sparse Non-symmetric System of Linear Equations ⋮ Sensitivity analyses for factorizations of sparse or structured matrices ⋮ Structured condition numbers for some matrix factorizations of structured matrices ⋮ Structured condition numbers and statistical condition estimation for the \(LDU\) factorization ⋮ Perturbation and error analyses of the partitioned \textit{LU} factorization for block tridiagonal linear systems ⋮ Improved rigorous perturbation bounds for the LU and QR factorizations ⋮ Mixed and componentwise condition numbers for matrix decompositions ⋮ Perturbations of Triangular Matrix Factorizations ⋮ An efficient method for constructing an ILU preconditioner for solving large sparse nonsymmetric linear systems by the GMRES method ⋮ Stability and sensitivity of tridiagonal LU factorization without pivoting ⋮ \(LU\)-decomposition and numerical structure for solving large sparse nonsymmetric linear systems ⋮ Perturbation bounds for triangular and full rank factorizations

Uses Software

• mctoolbox

Cites Work

• Unnamed Item
• Perturbation bounds for the \(LDL^ H\) and LU decompositions
• Sensitivity analyses for factorizations of sparse or structured matrices
• Componentwise perturbation bounds for some matrix decompositions
• Condition numbers and equilibration of matrices
• On the perturbation of LU and Cholesky factors
• On the Perturbation of LU, Cholesky, and QR Factorizations
• Perturbation Analyses for the QR Factorization
• New perturbation analyses for the Cholesky factorization