90 research outputs found
Embedded techniques for choosing the parameter in Tikhonov regularization
This paper introduces a new strategy for setting the regularization parameter
when solving large-scale discrete ill-posed linear problems by means of the
Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy
principle, although no initial knowledge of the norm of the error that affects
the right-hand side is assumed; an increasingly more accurate approximation of
this quantity is recovered during the Arnoldi algorithm. Some theoretical
estimates are derived in order to motivate our approach. Many numerical
experiments, performed on classical test problems as well as image deblurring
are presented
Some transpose-free CG-like solvers for nonsymmetric ill-posed problems
2siThis 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.openembargoed_20210328Gazzola S.; Novati P.Gazzola, S.; Novati, P
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