@book{6ca6827723b7456eb620dd58324b66b1,
title = "Accelerating the Induced Dimension Reduction method using spectral information",
abstract = "The Induced Dimension Reduction method (IDR(s)) [1] is a short-recurrences Krylov method to solve systems of linear equations. In this work, we accelerate this method using the spectral information. We construct a Hessenberg relation from the IDR(s) residual recurrences formulas, from which we approximate the eigenvalues and eigenvectors. Using the Ritz values, we propose a self-contained variant of the Ritz-IDR((s) method [2] for solving a system of linear equations. In addition, the Ritz vectors are used to speed-up IDR(s) in the solution of a sequence of linear systems.",
keywords = "Induced Dimension, Reduction method, system of linear equations, sequence of systems of linear equation, eigenvalues and eigenvectors",
author = "R. Astudillo and {de Gier}, J.M. and {van Gijzen}, M.B.",
year = "2017",
language = "English",
series = "Reports of the Delft Institute of Applied Mathematics",
publisher = "Delft University of Technology",
address = "Netherlands",
}