Two-sided and alternating Jacobi-Davidson - Hochstenbach, Michiel Erik; Sleijpen, G.L.G. (My University, 2001)
We discuss two variants of a two-sided Jacobi-Davidson method, which have asymptotically cubic convergence for nonnormal matrices and aim to find both right and left eigenvectors. These methods can be seen as Jacobi-Davidson analogs of Ostrowskis two-sided Rayleigh Quotient Iteration. Some relations between (exact and inexact) two-sided Jacobi-Davidson and (exact and inexact) two-sided Rayleigh Quotient Iteration are given, together with convergence rates. Furthermore, we introduce an alternating Jacobi-Davidson process, that can be seen as the Jacobi-Davidson analog of Parletts alternating Rayleigh Quotient Iteration. The methods are extended to the generalized and polynomial eigenproblem. Advantages of the methods are illustrated by numerical examples.
Keywords: Wiskunde en Informatica; JacobiDavidson; Rayleigh Quotient Iteration; Ostrowskis two-sided Rayleigh Quotient Iteration; Parletts alternating Rayleigh Quotient Iteration; two-sided Lanczos; correction equation; nonnormal matrix; inexact accelerated Newton method; rate of convergence; generalized eigenproblem; polynomial eigenproblem