|
Applied Math Seminar
Convergence and Shift Behavior for Arnoldi Eigenvalue Computations
|
|
The restarted Arnoldi algorithm is among the most widespread methods for computing a subset of the eigenvalues of large, nonsymmetric matrices, thanks to its robust implementation in ARPACK and MATLAB's "eigs" command. While the method is highly effective in practice, its convergence behavior can be rather exotic. In this talk we shall explain the factors that control convergence (number and location of the sought-after eigenvalues, nonnormality, starting vector), indicate why a complete convergence theory has proved so elusive through examples that cause the method to fail in exact arithmetic, and describe some restrictive sufficient conditions that ensure convergence. (This work is a collaboration with Russell Carden.) |