A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations

DOI10.1007/BF01941141zbMath0658.65041MaRDI QIDQ1111337

Åke Björck

Publication date: 1988

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

comparison of methodsregularizationconjugate gradient methodcross-validationleast squares problemsLanczos bidiagonalizationill-conditioned systems

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Uses Software

• LSQR
• LINPACK
• CRAIG

Cites Work

• The block conjugate gradient algorithm and related methods
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses
• The Singular Value Decomposition in Product Form
• Some Superlinear Convergence Results for the Conjugate Gradient Method
• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix
• A Bidiagonalization-Regularization Procedure for Large Scale Discretizations of Ill-Posed Problems
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
• Algorithms for the regularization of ill-conditioned least squares problems
• The Lanczos Algorithm with Selective Orthogonalization
• A Practical Examination of Some Numerical Methods for Linear Discrete Ill-Posed Problems
• Calculating the Singular Values and Pseudo-Inverse of a Matrix