  Recently, a kind of eigensolvers based on contour integral were developed for
computing the eigenvalues inside a given region in the complex plane. The CIRR
method is a classic example among this kind of methods. In this paper, we
propose a contour-integral based QZ method which is also devoted to computing
partial spectrum of generalized eigenvalue problems. Our new method takes
advantage of the technique in the CIRR method of constructing a particular
subspace containing the eigenspace of interest via contour integrals. The main
difference between our method and CIRR is the mechanism of extracting the
desired eigenpairs. We establish the related framework and address some
implementation issues so as to make the resulting method applicable in
practical implementations. Numerical experiments are reported to illustrate the
numerical performance of our new method.
