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Title: Regularization matrices for discrete ill-posed problems in several space dimensions: Regularization matrices for discrete ill-posed problems in several space dimensions
Authors:
 ;  ;  ;  
Award ID(s):
1729509 1720259
Publication Date:
NSF-PAR ID:
10055011
Journal Name:
Numerical Linear Algebra with Applications
Volume:
25
Issue:
4
Page Range or eLocation-ID:
e2163
ISSN:
1070-5325
Publisher:
Wiley Blackwell (John Wiley & Sons)
Sponsoring Org:
National Science Foundation
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  1. Abstract Randomized methods can be competitive for the solution of problems with a large matrix of low rank. They also have been applied successfully to the solution of large-scale linear discrete ill-posed problems by Tikhonov regularization (Xiang and Zou in Inverse Probl 29:085008, 2013). This entails the computation of an approximation of a partial singular value decomposition of a large matrix A that is of numerical low rank. The present paper compares a randomized method to a Krylov subspace method based on Golub–Kahan bidiagonalization with respect to accuracy and computing time and discusses characteristics of linear discrete ill-posed problems thatmore »make them well suited for solution by a randomized method.« less