Open AccessRational Krylov for Nonlinear Eigenproblems, an Iterative Projection Method
Author(s) -
Elias Jarlebring,
Heinrich Voß
Publication year - 2005
Publication title -
applications of mathematics
Language(s) - English
Resource type - Journals
eISSN - 1572-9109
pISSN - 0862-7940
DOI - 10.1007/s10492-005-0036-9
Subject(s) - mathematics , krylov subspace , generalized minimal residual method , arnoldi iteration , iterative method , solver , nonlinear system , projection (relational algebra) , projection method , mathematical optimization , algorithm , dykstra's projection algorithm , quantum mechanics , physics
In recent papers Ruhe (10), (12) suggested a rational Krylov method for nonlinear eigenproblems knitting together a secant method for linearizing the nonlinear problem and the Krylov method for the linearized problem. In this note we point out that the method can be understood as an iterative projection method. Similar to the Arnoldi method presented in (13), (14) the search space is expanded by the direction from residual inverse iteration. Numerical methods demonstrate that the rational Krylov method can be accelerated considerably by replacing an inner iteration by an explicit solver of projected problems.
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