An improved preconditioned LSQR for discrete ill-posed problems

Authors:
Angelika Bunse-Gerstner;Valia Guerra-Ones;Humberto Madrid de La Vega
Affiliations:
Center of Technomathematic, University of Bremen, Germany;Instituto de Cibernetica, Matematica y Fisica, Havana, Cuba;Centro de Investigaciones en Matemáticas Aplicadas, Saltillo, México
Venue:
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
Year:
2006

Citing 7
Cited 0

Ten lectures on wavelets

Ten lectures on wavelets
Analysis of discrete ill-posed problems by means of the L-curve

SIAM Review
The Discrete Cosine Transform

SIAM Review
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion

Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Near-Optimal Parameters for Tikhonov and Other Regularization Methods

SIAM Journal on Scientific Computing
Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems

SIAM Journal on Matrix Analysis and Applications
Algorithm 827: irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix

ACM Transactions on Mathematical Software (TOMS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a modified version of the two-level iterative method proposed in [M. Hanke, R. Vogel, Two-level preconditioners for regularized inverse problems. I: Theory, Numerische Mathematik 83 (1999) 385-402]. Here, we propose the application of the two-level Schur complement CG on the unregularized problem and the introduction of the regularization process for solving only one of the linear systems produced by the algorithm. The modified algorithm is substantially cheaper and numerical examples show similar approximations in both cases. A novel basis for the coarse subspace is incorporated in the analysis. Numerical experiments for some test problems and a practical scattering problem are presented.