On the augmented system approach to sparse least-squares problems

DOI10.1007/BF01389335zbMath0678.65024MaRDI QIDQ1124275

P. P. M. de Rijk, Mario Arioli, Iain S. Duff

Publication date: 1989

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133376

zbMATH Keywords

numerical resultserror analysiscondition numberscalingnormal equationstest matricesleast-squares problemIterative refinements

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items

A class of modified GSS preconditioners for complex symmetric linear systems, Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems, Enhancing Block Cimmino for Sparse Linear Systems with Dense Columns via Schur Complement, Corrected sequential linear programming for sparse minimax optimization, Solution of augmented linear systems using orthogonal factorizations, Efficient Preconditioners for Interior Point Methods via a New Schur Complement-Based Strategy, Solution of sparse rectangular systems using LSQR and Craig, A parameterized shift-splitting preconditioner for saddle point problems, A Novel Partitioning Method for Accelerating the Block Cimmino Algorithm, Symmetric SOR method for augmented systems, Semi-convergence analysis of GMSSOR methods for singular saddle point problems, Componentwise analysis of direct factorization of real symmetric and Hermitian matrices, On Using Cholesky-Based Factorizations and Regularization for Solving Rank-Deficient Sparse Linear Least-Squares Problems, A class of new extended shift-splitting preconditioners for saddle point problems, Convergence of a generalized MSSOR method for augmented systems, Convergence of relaxation iterative methods for saddle point problem, Preconditioning indefinite systems in interior point methods for large scale linear optimisation, Interior point methods 25 years later, A modified symmetric successive overrelaxation method for augmented systems, Generalized AOR method for solving a class of generalized saddle point problems, The solution of large-scale least-squares problems on supercomputers, Iterative refinement enhances the stability of \(QR\) factorization methods for solving linear equations, Selection of fictitious independent variables for the solution of sparse linear equations, On generalized symmetric SOR method for augmented systems, Variants of the Uzawa method for three-order block saddle point problem, On condition numbers for Moore–Penrose inverse and linear least squares problem involving Kronecker products, On the GTSOR-like Method for the Augmented systems, A condition analysis of the weighted linear least squares problem using dual norms, Regularization and preconditioning of KKT systems arising in nonnegative least-squares problems, Improved componentwise verified error bounds for least squares problems and underdetermined linear systems, Symmetric-triangular decomposition and its applications. II: Preconditioners for indefinite systems, Implementing cholesky factorization for interior point methods of linear programming, A survey of direct methods for sparse linear systems, A class of Uzawa-SOR methods for saddle point problems, Exploiting structure in parallel implementation of interior point methods for optimization, On the minimum convergence factor of a class of GSOR-like methods for augmented systems, Using dual techniques to derive componentwise and mixed condition numbers for a linear function of a linear least squares solution, Perturbation analysis of saddle-point problems, The augmented system variant of IPMs in two-stage stochastic linear programming computation, Perturbation bound of singular linear systems, Warm start of the primal-dual method applied in the cutting-plane scheme, The role of the augmented system in interior point methods, On mixed and componentwise condition numbers for Moore–Penrose inverse and linear least squares problems, A generalized shift-splitting preconditioner for saddle point problems, Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization, Component-wise perturbation analysis and error bounds for linear least squares solutions, Solving symmetric indefinite systems in an interior-point method for linear programming

Uses Software

• Harwell-Boeing sparse matrix collection

Cites Work

• A new polynomial-time algorithm for linear programming
• Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
• Jordan-Elimination und Ausgleichung nach kleinsten Quadraten
• Condition Estimates
• The Multifrontal Solution of Indefinite Sparse Symmetric Linear
• On the Method of Weighting for Equality-Constrained Least-Squares Problems
• A Survey of Condition Number Estimation for Triangular Matrices
• Sparse matrix test problems
• Scaling for Numerical Stability in Gaussian Elimination
• Iterative Refinement Implies Numerical Stability for Gaussian Elimination
• Solving Sparse Linear Systems with Sparse Backward Error
• Iterative refinement of linear least squares solutions I
• Unnamed Item
• Unnamed Item
• Unnamed Item