Perturbation and error analyses of the partitioned \textit{LU} factorization for block tridiagonal linear systems

DOI10.1007/s11253-017-1340-8zbMath1490.65087OpenAlexW2621367854MaRDI QIDQ1729410

Xianqiang Yang

Publication date: 27 February 2019

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-017-1340-8

zbMATH Keywords

perturbationblock tridiagonal matricesbackward error analysespartitioned LU factorization

Mathematics Subject Classification ID

Factorization of matrices (15A23) Numerical linear algebra (65F99)

Related Items

Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method ⋮ Efficient and linear schemes for anisotropic Cahn-Hilliard model using the stabilized-invariant energy quadratization (S-IEQ) approach ⋮ Efficient linear schemes for the nonlocal Cahn-Hilliard equation of phase field models ⋮ Regularized linear schemes for the molecular beam epitaxy model with slope selection ⋮ Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the magneto-hydrodynamic equations ⋮ Efficient, non-iterative, and second-order accurate numerical algorithms for the anisotropic Allen-Cahn equation with precise nonlocal mass conservation

Uses Software

• mctoolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Perturbation bounds for the \(LDL^ H\) and LU decompositions
• On the sensitivity of the LU factorization
• A new approach to backward error analysis of LU factorization
• Stability of the matrix factorization for solving block tridiagonal symmetric indefinite linear systems
• Stability and sensitivity of tridiagonal LU factorization without pivoting
• On the perturbation of LU and Cholesky factors
• On the Perturbation of LU, Cholesky, and QR Factorizations
• The stability of LU-decompositions of block tridiagonal matrices
• Perturbation Bounds for the $QR$ Factorization of a Matrix
• Perturbation Analyses for the QR Factorization
• Stability of block algorithms with fast level-3 BLAS
• The Accuracy of Solutions to Triangular Systems
• Stability of block LU factorization
• Stability of Symmetric Ill-Conditioned Systems Arising in Interior Methods for Constrained Optimization
• Perturbation Theory for Factorizations of LU Type through Series Expansions