Induced Dimension Reduction method for solving linear matrix equations

This paper discusses the solution of large-scale linear matrix equations using the Induced Dimension reduction method (IDR(s)). IDR(s) was originally presented to solve system of linear equations, and is based on the IDR(s) theorem. We generalize the IDR(s) theorem to solve linear problems in any finite-dimensional space. This generalization...

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....