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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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书目名称Handbook for Automatic Computation
副标题Volume II: Linear Al
编辑J. H. Wilkinson,C. Reinsch,F. L. Bauer,A. S. House
视频video
丛书名称Grundlehren der mathematischen Wissenschaften
图书封面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
描述The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentation of the basic algorithms in some specific areas of numerical analysis. This is the first such volume and it was feIt that the topic Linear Algebra was a natural choice, since the relevant algorithms are perhaps the most widely used in numerical analysis and have the advantage of forming a weil defined dass. The algorithms described here fall into two main categories, associated with the solution of linear systems and the algebraic eigenvalue problem respectively and each set is preceded by an introductory chapter giving a comparative assessment.
出版日期Book 1971
关键词ALGOL; Algol W; Calculation; Finite; Natural; algebra; algorithms; computer; eigenvalue problem; equation; num
版次1
doihttps://doi.org/10.1007/978-3-642-86940-2
isbn_softcover978-3-642-86942-6
isbn_ebook978-3-642-86940-2Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 1971
The information of publication is updating

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Rational , Transformation with Newton Shift for Symmetric Tridiagonal Matricesd throughout 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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Book 1971henever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentati
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Grundlehren der mathematischen Wissenschaftenhttp://image.papertrans.cn/h/image/420737.jpg
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https://doi.org/10.1007/978-94-009-1569-5Let . be a real .×. matrix and.the induced mapping ..→... If ..ǂ0, then one can solve the first of these equations for .. and insert the result into the remaining equations.
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https://doi.org/10.1007/978-3-642-56257-0In an earlier paper in this series [2] the triangular factorization of positive definite band matrices was discussed. With such matrices there is no need for pivoting, but with non-positive definite or unsymmetric matrices pivoting is necessary in general, otherwise severe numerical instability may result even when the matrix is well-conditioned.
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