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Title: On refined Ritz vectors and polynomial characterization
Authors: Ravibabu, M.
Singh, A.
Keywords: Refined Ritz vectors
Refined Arnoldi method
Polynomial characterization
Issue Date: 2014
Citation: Computers and Mathematics with Applications, 67(5), 1057-1064
Abstract: It is generally believed that the Ritz vectors do not coincide with the refined Ritz vectors in the Arnoldi method for computing eigenvalues of matrices. We show that this coincidence is theoretically possible. We provide a necessary and sufficient condition for this coincidence to happen and give examples to illustrate the same. Using Lanczos polynomials, we give a polynomial characterization of refined Ritz vectors of symmetric matrices that is different from the one available in the literature.
ISSN: 8981221
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