Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem

摘要

In this work we are interested in the numerical solution of the Quadratic Eigenvalue Problem (QEP) (λ~2M + λD + K)x = 0, where M, D, and K are given matrices of order N. Particularly, we study the applicability of the IDR(s) for eigenvalues to solve QEP. We present an IDR(s) algorithm that exploits the special block structure of the lin-ealized QEP to compute its eigenpairs. To this end we incorporate ideas from Second Order Arnoldi method proposed in [3].