Some Properties of the Arnoldi-Based Methods for Linear Ill-Posed Problems

DOI10.1137/16M106399XzbMath1367.65084MaRDI QIDQ5270353

Paolo Novati

Publication date: 23 June 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

algorithmGMREScompact operatorArnoldi algorithmlinear ill-posed problemHilbert-Schmidt operatordominant singular values

Mathematics Subject Classification ID

Linear operators defined by compactness properties (47B07) Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (6)

Krylov methods for inverse problems: Surveying classical, and introducing new, algorithmic approaches ⋮ Rational Krylov and ADI iteration for infinite size quasi-Toeplitz matrix equations ⋮ A Convergence Result for Some Krylov–Tikhonov Methods in Hilbert Spaces ⋮ Some transpose-free CG-like solvers for nonsymmetric ill-posed problems ⋮ Arnoldi decomposition, GMRES, and preconditioning for linear discrete ill-posed problems ⋮ Convergence analysis of LSQR for compact operator equations

Uses Software

• LSQR
• Regularization tools
• UTV

Cites Work

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• Inheritance of the discrete Picard condition in Krylov subspace methods
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• On Krylov projection methods and Tikhonov regularization
• Regularization tools version \(4.0\) for matlab \(7.3\)
• Embedded techniques for choosing the parameter in Tikhonov regularization
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• The Use of Auto-correlation for Pseudo-rank Determination in Noisy III-conditioned Linear Least-squares Problems
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• A Note on the Superlinear Convergence of GMRES
• A Regularization Parameter in Discrete Ill-Posed Problems
• Superlinear Convergence of Krylov Subspace Methods for Self-Adjoint Problems in Hilbert Space
• On the Occurrence of Superlinear Convergence of Exact and Inexact Krylov Subspace Methods
• Global Convergence of the Basic QR Algorithm On Hessenberg Matrices
• A Theoretical Comparison of the Arnoldi and GMRES Algorithms

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