Titlebook: Linear Algebra; J. H. Wilkinson,C. Reinsch,F. L. Bauer (Chief edit Book 1971 Springer-Verlag Berlin Heidelberg 1971 algebra.linear algebra

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The , and , Algorithms for Symmetric Matricesis unitary and . is upper-triangular then . that is, . is unitarily similar to . By repeated application of the above result a sequence of matrices which are unitarily similar to a given matrix .. may be derived from the relations . and, in general, .. tends to upper-triangular form.

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Rational , Transformation with Newton Shift for Symmetric Tridiagonal Matricesroughout the iteration. Thus, the . step may be achieved by two successive Cholesky . steps or equivalently, since the matrix is tridiagonal, by two . steps which are numerically stable [4] and avoid square roots. The rational . step used here needs slightly fewer additions than the Ortega-Kaiser step [3].

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Handbook for Automatic Computationhttp://image.papertrans.cn/l/image/586252.jpg

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https://doi.org/10.1007/978-3-662-39778-7algebra; linear algebra; mathematics; optimization; matrix theory

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Iterative Refinement of the Solution of a Positive Definite System of Equations based on the Cholesky factorization of . is ill-conditioned the computed solution may not be sufficiently accurate, but (provided . is not almost singular to working accuracy) it may be improved by an iterative procedure in which the Cholesky decomposition is used repeatedly.

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