On the error analysis and implementation of some eigenvalue decomposition and singular value decomposition algorithms

摘要: Many algorithms exist for computing the symmetric eigendecomposition, singular value decomposition and generalized decomposition. In this thesis, we present several new improvements on old algorithms, analyzing them with respect to their speed, accuracy, storage requirements. We first discuss variations bisection algorithm finding eigenvalues of tridiagonal matrices. then a fast implementation using parallel prefix. also possible ways stabilize it by iterative refinement. Finally, how use divide-and-conquer compute solve linear least squares problem implement Van Loan''s algorithm.