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Titlebook: Handbook for Automatic Computation; Volume II: Linear Al J. H. Wilkinson,C. Reinsch,F. L. Bauer,A. S. House Book 1971 Springer-Verlag Berli

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The Science of Construction Materials has been described first by Stiefel and Hesteness [1, 2] and additional information is contained in [3] and [4]. The notations used here coincide partially with those used in [5] where also the connexions with other methods and generalisations of the CG-algorithm are presented.
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https://doi.org/10.1007/978-3-319-92796-1 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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Iterative Refinement of the Solution of a Positive Definite System of Equationsas based on the Cholesky factorization of .. If A is ill-conditioned the computed solution may not be sufficiently accurate, but (provided A 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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The Conjugate Gradient Method has been described first by Stiefel and Hesteness [1, 2] and additional information is contained in [3] and [4]. The notations used here coincide partially with those used in [5] where also the connexions with other methods and generalisations of the CG-algorithm are presented.
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Householder’s Tridiagonalization of a Symmetric Matrixd since its publication and in view of its importance it seems worthwhile to issue improved versions of the procedure given there. More than one variant is given since the most efficient form of the procedure depends on the method used to solve the eigenproblem of the derived tridiagonal matrix.
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