A preconditioned block conjugate gradient algorithm for computing extreme eigenpairs of symmetric and Hermitian problems
نویسندگان
چکیده
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.
منابع مشابه
Preconditioned Techniques for Large Eigenvalue Problems a Thesis Submitted to the Faculty of the Graduate School of the University of Minnesota by Kesheng Wu in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
This research focuses on nding a large number of eigenvalues and eigenvectors of a sparse symmetric or Hermitian matrix, for example, nding 1000 eigenpairs of a 100,000 100,000 matrix. These eigenvalue problems are challenging because the matrix size is too large for traditional QR based algorithms and the number of desired eigenpairs is too large for most common sparse eigenvalue algorithms. I...
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