A projection method for generalized eigenvalue problems using numerical integration.
The paper deals with the computational aspects of the generalized eigenvalue problem \(A=\lambda B\) where \(A\) and \(B\) are large \(n\times n\;\) matrices. The authors use the resolvent operator to construct a Weyl characteristic function whose poles are the eigenvalues. As expected, classical root finding methods fail when the eigenvalues are not real. To this end the authors compute contour integrals numerically and using the residue theorem to can detect and locate these eigenvalues. The error corresponding to the trapezoidal rule is analyzed and various examples can be found at the end of the paper.
scientific article; zbMATH DE number 1993206