1,720,974 research outputs found
A Convergence Result for Some Krylov–Tikhonov Methods in Hilbert Spaces
No full textIn this paper, we present a convergence result for some Krylov
projection methods when applied to the Tikhonov minimization
problem in its general form. In particular,we consider the method
based on the Arnoldi algorithm and the one based on the Lanczos
bidiagonalization process
Preface of the "Young Researchers Symposium on Numerical Methods for Differential Problems of Practical Interest"
No full textPreface of the "Young Researchers Symposium on Numerical Methods for Differential Problems of Practical Interest
On Krylov solutions to infinite-dimensional inverse linear problems
No full textWe discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of a given inverse problem, together with a series of model examples and numerical experiments
A fast and simple algorithm for the computation of the Lerch transcendent
No full textThis paper deals with the computation of the Lerch transcendent by means of the GaussLaguerre formula. An a priori estimate of the quadrature error, that allows to compute the number of quadrature nodes necessary to achieve an arbitrary precision, is derived. Exploiting the properties of the Gauss-Laguerre rule and the error estimate, a truncated approach is also considered. The algorithm used and its Matlab implementation are reported. The numerical examples confirm the reliability of this approach
Some transpose-free CG-like solvers for nonsymmetric ill-posed problems
Full text linkThis 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
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