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Numerical solution of large nonsymmetric eigenvalue problems. (English) Zbl 0798.65053
Summary: We describe several methods based on combinations of Krylov subspace techniques, deflation procedures and preconditionings, for computing a small number of eigenvalues and eigenvectors or Schur vectors of large sparse matrices. The most effective techniques for solving realistic problems from applications are those methods based on some form of preconditioning and one of several Krylov subspace techniques, such as Arnoldi’s method or the Lanczos procedure.
We consider two forms of preconditionings: shift-and-invert and polynomial acceleration. The latter presents some advantages for parallel/vector processing but may be ineffective if eigenvalues inside the spectrum are sought. We provide some algorithmic details that improve the reliability and effectiveness of these techniques.

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F50 Computational methods for sparse matrices
Software:
SRRIT
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