Version 1.2.2

22nd February 2023

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EB22: Sparse unsymmetric: subspace iteration

Given a real unsymmetric \(n \times n\) matrix \(\mathbf{A} = {\{a_{ij}\}}\), this routine uses subspace iteration to calculate the \(r\) eigenvalues \(\lambda _i\), \(i = 1, 2,..., r\), that are right-most, left-most, or are of largest modulus. The right-most (respectively, left-most) eigenvalues are the eigenvalues with the most positive (respectively, negative) real part. A second entry will return the associated eigenvectors \(\mathbf{y} _i\), \(i = 1, 2,..., r\), where \(\mathbf{Ay} _i = \lambda _i \mathbf{y} _i\). The routine may also be used to calculate a group of eigensolutions elsewhere in the spectrum.