Edited by: F. Magoulès

Keywords: algebraic model reduction, Arnoldi method, Padé via Lanczos method, Krylov methods, iterative linear system solver, modal truncation.

This chapter reviews numerical methods for efficiently computing frequency response functions. The focus is on the Padé via Lanczos and Arnoldi methods and their application to vibration problems, which may lead to significant speed-ups. Examples are given to illustrate the theory, as well as a bibliographical note for further study.

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