RAL-TR-2010-019 A preconditioned block conjugate gradient algorithm for computing extreme eigenpairs of symmetric and Hermitian problems

This report describes an algorithm for the efficient computation of several extreme eigenvalues and corresponding eigenvectors of a large-scale standard or generalized real symmetric or complex Hermitian eigenvalue problem. The main features are: (i) a new conjugate gradient scheme specifically designed for eigenvalue computation; (ii) the use of the preconditioning as a cheaper alternative to matrix factorization for large discretized differential problems; (iii) simultaneous computation of several eigenpairs by subspace iteration; and (iv) the use of efficient stopping criteria based on error estimation rather than the residual tolerance.

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