Solution of sparse rectangular systems using LSQR and Craig

DOI10.1007/BF01739829zbMath0844.65029MaRDI QIDQ1907877

Michael A. Saunders

Publication date: 18 March 1996

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

regularizationconjugate gradient methoddirect methodLSQRGolub-Kahan bidiagonalizationLanczos processunderdetermined systemsdamped least-squares problemssparse linear equationsleast squares QR factorizationoverdetetermined systemssparse rectangular systems

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical solutions to overdetermined systems, pseudoinverses (65F20)

Related Items

Preconditioning Linear Least-Squares Problems by Identifying a Basis Matrix, A Computational Study of Using Black-box QR Solvers for Large-scale Sparse-dense Linear Least Squares Problems, Implicit iterative schemes based on augmented linear systems, Noise representation in residuals of LSQR, LSMR, and CRAIG regularization, CVXGEN: a code generator for embedded convex optimization, On Using Cholesky-Based Factorizations and Regularization for Solving Rank-Deficient Sparse Linear Least-Squares Problems, Deflation for the Off-Diagonal Block in Symmetric Saddle Point Systems, A Class of Approximate Inverse Preconditioners Based on Krylov-Subspace Methods for Large-Scale Nonconvex Optimization, A fast implementation for GMRES method, Sharp 2-Norm Error Bounds for LSQR and the Conjugate Gradient Method, Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations, Computing projections with LSQR, Regularization and preconditioning of KKT systems arising in nonnegative least-squares problems, A primal-dual regularized interior-point method for convex quadratic programs, Minimum residual methods for augmented systems, LNLQ: An Iterative Method for Least-Norm Problems with an Error Minimization Property, Simple stopping criteria for the LSQR method applied to discrete ill-posed problems, Euclidean-Norm Error Bounds for SYMMLQ and CG, LSLQ: An Iterative Method for Linear Least-Squares with an Error Minimization Property, Modifying the inertia of matrices arising in optimization, Solving large linear least squares problems with linear equality constraints, Analysis of approximate inverses in tomography. II: Iterative inverses

Uses Software

• LSQR
• SPARSE-QR
• CRAIG

Cites Work

• On the augmented system approach to sparse least-squares problems
• Unsymmetric positive definite linear systems
• A Storage-Efficient Algorithm for Finding the Regularized Solution of a Large, Inconsistent System of Equations
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Solution of Sparse Indefinite Systems of Linear Equations
• Exploiting zeros on the diagonal in the direct solution of indefinite sparse symmetric linear systems
• Sparse QR factorization in MATLAB
• On Row Relaxation Methods for Large Constrained Least Squares Problems
• Test Matrices for Regularization Methods
• Symmetric Quasidefinite Matrices
• On the Stability of Cholesky Factorization for Symmetric Quasidefinite Systems
• Iterative refinement of linear least squares solutions I
• Calculating the Singular Values and Pseudo-Inverse of a Matrix
• The N‐Step Iteration Procedures
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