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Some transpose-free CG-like solvers for nonsymmetric ill-posed problems

Silvia Gazzola and Paolo Novati

Abstract

This paper introduces and analyzes an original class of Krylov subspace methods that provide an efficient alternative to many well-known conjugate-gradient-like (CG-like) Krylov solvers for square nonsymmetric linear systems arising from discretizations of inverse ill-posed problems. The main idea underlying the new methods is to consider some rank-deficient approximations of the transpose of the system matrix, obtained by running the (transpose-free) Arnoldi algorithm, and then apply some Krylov solvers to a formally right-preconditioned system of equations. Theoretical insight is given, and many numerical tests show that the new solvers outperform classical Arnoldi-based or CG-like methods in a variety of situations.

JEL Classification: 65F10; 65F22

  1. Funding: This work was partially supported by GNCS-INdAM and FRA-University of Trieste. P. Novati is a member of the INdAM research group GNCS.

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Received: 2018-10-09
Revised: 2019-05-31
Accepted: 2019-11-20
Published Online: 2019-12-31
Published in Print: 2020-03-26

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