Chapter 57
The Implicitly Restarted Arnoldi Method
D. C. Sorensen
Rice University
The implicitly restarted Arnoldi method (IRAM) [Sor92] is a variant of Arnoldi’s method for computing a selected subset of eigenvalues and corresponding eigenvectors for large matrices. Implicit restarting is a synthesis of the implicitly shifted QR iteration and the Arnoldi process that effectively limits the dimension of the Krylov subspace required to obtain good approximations to desired eigenvalues. The space is repeatedly expanded and contracted with each new Krylov subspace generated by an updated starting vector obtained by implicit application of a matrix polynomial to the old starting vector. This process is designed to filter out undesirable components ...
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