SPECTRAL DECOMPOSITION Genera Notions Decompositions Spectral Sets of Finite Type Adjoint and Product Spaces SPECTRAL APPROXIMATION Convergence of operators Property U Property L Error Estimates IMPROVEMENT OF ACCURACY Iterative Refinement Acceleration FINITE RANK APPROXIMATIONS Approximations Based on Projection Approximations of Integral Operators A Posteriori Error Estimates MATRIX FORMULATIONS Finite Rank Operators Iterative Refinement Acceleration Numerical Examples MATRIX COMPUTATIONS QR Factorization Convergence of a Sequence of Subspaces QR Methods and Inverse Iteration Error Analysis REFERENCES INDEX Each chapter also includes exercises