Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh–Ritz procedure for generalized Hermitian eigenvalue problems

We propose a verified computation method for eigenvalues in region and the corresponding eigenvectors of generalized Hermitian eigenvalue problems. The proposed uses complex moments to extract eigencomponents interest from random matrix Rayleigh$\unicode{x2013}$Ritz procedure project given problem into reduced problem. moment is by contour integral approximated using numerical quadrature. split error truncation quadrature rounding errors evaluate each. This idea evaluation inherits our previous Hankel approach, whereas enables verification requires half number points approach reduce same order. Moreover, forms transformation that eigenvectors. Numerical experiments show faster than methods while maintaining performance works even nearly singular pencils presence multiple eigenvalues.