Let X be a symmetric space of noncompact type whose isometry group is either SU(n, 1) or Spin(2n, 1). Then the Dirac operator D is defined on L2-sections of certain homogeneous vector bundles over X.

In this paper we consider approximate eigenvalues and approximate eigenspaces for the generalized Rayleigh quotient, and present some residual bounds. Our obtained bounds will improve the existing ...