Krylov type subspace methods for matrix polynomials

Citations of this article
Mendeley users who have this article in their library.


We consider solving eigenvalue problems or model reduction problems for a quadratic matrix polynomial Iλ2 - Aλ - B with large and sparse A and B. We propose new Arnoldi and Lanczos type processes which operate on the same space as A and B live and construct projections of A and B to produce a quadratic matrix polynomial with the coefficient matrices of much smaller size, which is used to approximate the original problem. We shall apply the new processes to solve eigenvalue problems and model reductions of a second order linear input-output system and discuss convergence properties. Our new processes are also extendable to cover a general matrix polynomial of any degree. © 2005 Elsevier Inc. All rights reserved.




Hoffnung, L., Li, R. C., & Ye, Q. (2006). Krylov type subspace methods for matrix polynomials. Linear Algebra and Its Applications, 415(1), 52–81.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free