Qr Convergence Theory and Practice
نویسنده
چکیده
The family of GR algorithms is discussed. This includes the standard and multishift QR and LR algorithms, the Hamiltonian QR algorithm, divide-and-conquer algorithms such as the matrix sign function method, and many others. Factors that aaect convergence are the quality of the transforming matrices and ratios of eigenvalues. Implicit implementations as bulge-chasing algorithms are discussed, as is the mechanism by which information about shifts is transmitted in the bulge. In the presence of roundoo errors this mechanism works well if the degree is small and poorly if the degree is large.
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