LSLQ: An Iterative Method for Linear Least-Squares with an Error Minimization Property

DOI10.1137/17M1113552zbMath1451.65028OpenAlexW2911643836MaRDI QIDQ3119540

Dominique Orban, Ron Estrin, Michael A. Saunders

Publication date: 12 March 2019

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1113552

zbMATH Keywords

error minimizationleast-squares problemserror bound estimates

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22) Least squares and related methods for stochastic control systems (93E24) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Linear equations (linear algebraic aspects) (15A06) Orthogonalization in numerical linear algebra (65F25)

Related Items

Discrete vector calculus and Helmholtz Hodge decomposition for classical finite difference summation by parts operators, LSMB: Minimizing the Backward Error for Least-Squares Problems, BiLQ: An Iterative Method for Nonsymmetric Linear Systems with a Quasi-Minimum Error Property, Implementing a Smooth Exact Penalty Function for Equality-Constrained Nonlinear Optimization, Sharp 2-Norm Error Bounds for LSQR and the Conjugate Gradient Method, Data-Driven Modeling for Wave-Propagation, Unnamed Item, LAP: a Linearize and Project Method for Solving Inverse Problems with Coupled Variables, LNLQ: An Iterative Method for Least-Norm Problems with an Error Minimization Property, Euclidean-Norm Error Bounds for SYMMLQ and CG, <scp>TriCG</scp> and <scp>TriMR</scp>: Two Iterative Methods for Symmetric Quasi-definite Systems

Uses Software

• LSQR
• FACTORIZE
• LSMR
• MINRES
• CRAIG

Cites Work

• Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods
• On error estimation in the conjugate gradient method and why it works in finite precision computations
• Solution of sparse rectangular systems using LSQR and Craig
• Estimates of the \(l_2\) norm of the error in the conjugate gradient algorithm
• A penalty method for PDE-constrained optimization in inverse problems
• Iterative Solution of Symmetric Quasi-Definite Linear Systems
• LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
• Euclidean-Norm Error Bounds for SYMMLQ and CG
• Algorithm 930
• Two Conjugate-Gradient-Type Methods for Unsymmetric Linear Equations
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Solution of Sparse Indefinite Systems of Linear Equations
• The QLP Approximation to the Singular Value Decomposition
• Trust Region Methods
• A Regularized Factorization-Free Method for Equality-Constrained Optimization
• Symmetric Quasidefinite Matrices
• Calculating the Singular Values and Pseudo-Inverse of a Matrix
• Methods of conjugate gradients for solving linear systems
• The N‐Step Iteration Procedures