The Induced Dimension Reduction method (IDR(s))  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  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.
|Name||Reports of the Delft Institute of Applied Mathematics|
- Induced Dimension
- Reduction method
- system of linear equations
- sequence of systems of linear equation
- eigenvalues and eigenvectors