We describe several methods based on combinations of Krylov subspace techniques, de-ation procedures and preconditionings, for computing a small number of eigenvalues and eigenvectors or Schur vectors of large sparse matrices. The most eective 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 ineective if eigenvalues inside the spectrum are sought. We provide some algorithmic details that improve the reliability and eectiveness of these techniques.
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1143
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Matrix Computations
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Iterative solution of linear equations in ODE codes
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