A theoretical comparison between inner products in the shift-invert Arnoldi method and the spectral transformation Lanczos method
This paper is concerned with the solution of generalized eigenvalue problems of the form: \[ Ax= \lambda Bx,\quad A,B\in \mathbb{R}^{n\times n},\quad x\neq 0, \] where \(A\) may be symmetric or non-symmetric, and \(B\) is symmetric positive (semi)definite, by the spectral transformation Lanczos method and the shift-invert Arnoldi method. The theory is illustrated by numerical examples arising from acoustic and structural finite element models. The theoretical results are extended to the Navier-Stokes problem.
scientific article; zbMATH DE number 1249447