Version 1.1.1

4th April 2013

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EB13 Sparse unsymmetric: Arnoldi’s method

Given a real unsymmetric n × n matrix A = {aij}, this routine uses Arnoldi based methods to calculate the r eigenvalues λi,i = 1,...,r, that are of largest absolute value, or are right-most, or are of largest imaginary parts. The right-most eigenvalues are those with the most positive real part. There is an option to compute the associated eigenvectors yi, i = 1,...,r, where Ayi = λiyi. The routine may be used to compute the left-most eigenvalues of A by using A in place of A.

The Arnoldi methods offered by EB13 are:

(1) The basic (iterative) Arnoldi method.
(2) Arnoldi’s method with Chebyshev acceleration of the starting vectors.
(3) Arnoldi’s method applied to the preconditioned matrix pl(A), where pl is a Chebyshev polynomial.

Each method is available in blocked and unblocked form.