Accelerating the Lanczos Algorithm via Polynomial Spectral Transformations
We consider the problem of computing a few clustered and/or interior eigenvalues of a symmetric matrix A without using a matrix factorization. This can be done by applying the Lanczos algorithm to p(A), where p(lambda) is a polynomial that maps the clustered and/or interior eigenvalues of A to extremal and well separated eigenvalues of p(A). We will demonstrate and compare several techniques of constructing these polynomials. Numerical examples are presented to illustrate the effectiveness of using these polynomial to accelerate the Lanczos process.
Citable link to this pagehttps://hdl.handle.net/1911/101895
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- CAAM Technical Reports