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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https://doi.org/10.1007/978-0-387-28822-2If . is a non-singular matrix then, in general, it can be factorized in the form . = ., where . is lower-triangular and . is upper-triangular. The factorization, when it exists, is unique to within a non-singular diagonal multiplying factor.

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https://doi.org/10.1007/978-3-319-41585-7Let . be a matrix of . rows and . columns, .≦.. If and only if the columns are linearly independent, then for any vector . there exists a unique vector . minimizing the Euclidean norm of ..

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https://doi.org/10.5822/978-1-61091-205-1In [1] an algorithm was described for carrying out the . algorithm for a real symmetric matrix using shifts of origin. This algorithm is described by the relations.where .. is orthogonal, .. is lower triangular and .. is the shift of origin determined from the leading 2×2 matrix of ...

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Symmetric Decomposition of a Positive Definite MatrixThe methods are based on the following theorem due to . [.].

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Symmetric Decomposition of Positive Definite Band MatricesThe method is based on the following theorem. If . is a positive definite matrix of band form such that.then there exists a real non-singular lower triangular matrix . such that