The nearest definite pair for the Hermitian generalized eigenvalue problem
Given a pair \((A,B)\) of Hermitian matrices of the same order, the authors give formulae for the nearest pair of Hermitian matrices that has a Crawford number greater or equal to a given positive value. The result is expressed in terms of the inner numerical radius associated with the field of values. Then they show how to exploit the result in order to solve the generalized eigenvalue problem \(Ax=\lambda Bx\) with nearly singular \(B\). The paper includes the algorithm and numerical examples.
scientific article; zbMATH DE number 1419860