A Restarted Induced Dimension Reduction method to approximate eigenpairs of large unsymmetric matrices

A new algorithm to compute eigenpairs of large unsymmetric matrices is presented. Using the Induced Dimension Reduction method (IDR), which was originally proposed for solving linear systems, we obtain a Hessenberg decomposition from which we approximate the eigen-values and eigenvectors of a matrix. This decomposition has two main advantages. First, the computational efficiency since IDR is a short recurrence method. Second, the IDR polynomial used to create this Hessenberg decomposition is also used as a filter to discard the unwanted eigenvalues. Additionally, we incorporate the implicitly restarting technique proposed by D.C. Sorensen, in order to approximate speciffic portions of the spectrum and improve the convergence.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc