Accelerating the Induced Dimension Reduction method using spectral information

R. Astudillo, J.M. de Gier, M.B. van Gijzen

Research output: Book/ReportReportProfessional


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.
Original languageEnglish
Place of PublicationDelft
PublisherDelft University of Technology
Number of pages25
Publication statusPublished - 2017

Publication series

NameReports of the Delft Institute of Applied Mathematics
ISSN (Print)1389-6520


  • Induced Dimension
  • Reduction method
  • system of linear equations
  • sequence of systems of linear equation
  • eigenvalues and eigenvectors


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