Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter April 5, 2013

TT-GMRES: solution to a linear system in the structured tensor format

S. V. Dolgov

Abstract

An adapted tensor-structured GMRES method for the TT format is proposed and investigated. The Tensor Train (TT) approximation is a robust approach to highdimensional problems. One class of such problems involves the solution of a linear system. In this work we study the convergence of the GMRES method in the presence of tensor approximations and provide relaxation techniques to improve its performance. Several numerical examples are presented. The method is also compared with a projection TT linear solver based on the ALS and DMRG methods. On a particular SPDE (high-dimensional parametric) problem these methods manifest comparable performance, with a good preconditioner the TT-GMRES overcomes the ALS solver.

Published Online: 2013-04-05
Published in Print: 2013-04

© 2013 by Walter de Gruyter GmbH & Co.

Scroll Up Arrow