Abstract
Iterative algorithms for the eigensolution of symmetric pencils of matrices are considered. It is shown that the symmetric Lanczos algorithm, the nonsymmetric Lanczos algorithm, and the Arnoldi algorithm are closely related in this case. The applicability of this class of algorithms to indefinite pencils is discussed. A new field of values concept is used to describe the symmetric pencil problem. Then spectral transformation corresponds to a rotation in the complex plane, and the inertia count gives the number of eigenvalues corresponding to points in one of two half planes.
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