Subspace Gap Residuals for Rayleigh–Ritz Approximations
Nela Bosner, Zlatko Drmač · SIAM Journal on Matrix Analysis and Applications · 2009
Large-scale eigenvalue and singular value computations are usually based on extracting information from a compression of the matrix to suitably chosen low dimensional subspaces. This paper introduces new a posteriori relative error bounds based on a residual expressed using the largest principal angle (gap) between relevant subspaces. The eigenvector approximations are estimated using subspace gaps and relative separation of the eigenvalues.