We use the two-dimensional discrete cosine transform to study how the noise from the data enters the reconstructed images computed by regularizing iterations, that is, Krylov subspace methods applied to discrete ill-posed problems. The regularization in these methods is obtained via the projection onto the associated Krylov subspace. We focus on CGLS/LSQR, GMRES, and RRGMRES, as well as MINRES ...

This work is devoted to fast and parameter-robust iterative solvers for frequency domain finite element equations, approximating the eddy current problem with harmonic excitation. We construct a preconditioned MinRes solver for the frequency domain equations, that is robust (= parameter– independent) in both the discretization parameter h and the frequency ω.

This paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints. We establish theory which shows that including a simple scaling within well-established block diagonal preconditioners for Stokes problems can result in significantly faster convergence when applying the preconditioned MINRES method. The codes used in the numerical studies ar...

Quantitative bounds are presented for the superlinear convergence of the MINRES method of Paige and Saunders [SIAM J. Numer. Anal., 1975] for the solution of sparse linear systems Ax = b, with A symmetric and indefinite. It is shown that the superlinear convergence is observed as soon as the harmonic Ritz values approximate well the eigenvalues of A that are either closest to zero or farthest f...

A ctitious domain method based on boundary Lagrange multipliers is proposed for linear elasticity problems in two dimensional domains. The solution of arising saddle-point problem is obtained iteratively using MINRES method with a positive deenite block diagonal preconditioner which is based on a fast direct solver for diiusion problems. Numerical experiments demonstrate the behavior of conside...

We use the two-dimensional DCT to study several properties of reconstructed images computed by regularizing iterations, that is, Krylov subspace methods applied to discrete ill-posed problems. The regularization in these methods is obtained via the projection onto the associated Krylov subspace. We focus on CGLS/LSQR, GMRES, and RRGMRES, as well as MINRES and MR-II in the symmetric case.