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Published in:
2010 | OriginalPaper | Chapter
Krylov Subspace Methods for the Eigenproblem
Authors : Howard C. Elman, Dianne P. O’Leary
Published in: G.W. Stewart
Publisher: Birkhäuser Boston
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These papers comprise some of Stewart’s recent contributions to the development and analysis of iterative algorithms based on Krylov subspace methods for computing eigenvalues. The task is to compute a few solutions (eigenvalues and eigenvectors) of the eigenvalue problem
$$\rm Av=\lambda v,$$
where
A
is an
$$n\times n$$
matrix, referenced through a matrix-vector product
$$\rm y\leftarrow Ax$$
. The focus in this work is on generalizing existing methods to clarify their properties and enhance stability. Much of this work was later integrated in a uniform manner into his volume on eigensystems (Chap. 5 of [GWS-B8]).