The nearest de®nite pair for the Hermitian generalized eigenvalue problem
نویسندگان
چکیده
The generalized eigenvalue problem Ax kBx has special properties when A;B is a Hermitian and de®nite pair. Given a general Hermitian pair A;B it is of interest to ®nd the nearest de®nite pair having a speci®ed Crawford number d > 0. We solve the problem in terms of the inner numerical radius associated with the ®eld of values of A iB. We show that once the problem has been solved it is trivial to rotate the perturbed pair A DA;B DB to a pair ~ A; ~ B for which kmin e B achieves its maximum value d, which is a numerically desirable property when solving the eigenvalue problem by methods that convert to a standard eigenvalue problem by ``inverting B''. Numerical examples are given to illustrate the analysis. Ó 1999 Elsevier Science Inc. All rights reserved.
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