Projection methods for solving large sparse eigenvalue problems

We present a unified approach to several methods for computing eigenvalues and eigenvectors of large sparse matrices. The methods considered are projection methods, i.e. Galerkin type methods, and include the most commonly used algorithms for solving large sparse eigenproblems like the Lanczos algorithm, Arnoldi's method and the subspace iteration. We first derive some a priori error bounds for general projection methods, in terms of the distance of the exact eigenvector from the subspace of approximation. Then this distance is estimated for some typical methods, particularly those for unsymmetric problems.

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