File Name: higham accuracy and stability of numerical algorithms .zip
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It also contains a good chapter on rounding error analysis and an interesting collection of exercises. The first analysis of floating point arithmetic was given by Samelson andBauer [, ]. Later in the same decade Carr [, ] gave a detaileddiscussion of error bounds for the basic arithmetic operations. An up-to-date and very readable reference on floating point arithmeticis the survey paper by Goldberg [, ], which includes a detailed discussion of IEEE arithmetic. The idea of representing floating point numbers in the form 2.
This book gives a thorough, up-to-date treatment of the behaviour of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. The coverage of the first edition has been expanded and updated, involving numerous improvements. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures. This new edition is a suitable reference for an advanced course and can also be used at all levels as a supplementary text from which to draw examples, historical perspective, statements of results, and exercises.
The effects of rounding errors on algorithms in numerical linear algebra have been much-studied for over fifty years, since the appearance of the first digital computers. The subject continues to occupy researchers, for several reasons. First, not everything is known about established algorithms. Second, new algorithms are continually being derived, and their behaviour in finite precision arithmetic needs to be understood. Third, new error analysis techniques lead to different ways of looking at and comparing algorithms, requiring a reassessment of conventional wisdom. Unable to display preview. Download preview PDF.
The Matrix Computation Toolbox is a collection of MATLAB M-files containing functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search optimization. Various other miscellaneous functions are also included. This toolbox supersedes the author's earlier Test Matrix Toolbox final release That book is the primary documentation for the toolbox: it describes much of the underlying mathematics and many of the algorithms and matrices it also describes many of the matrices provided by MATLAB's gallery function. The picture on the left, produced by toolbox function pscont , shows a view of pseudospectra of the matrix gallery 'triw', Nick Higham. Numerical Analysis Undergraduate Study Pathway.
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This book gives a thorough, up-to-date treatment of the behaviour of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. The coverage of the first edition has been expanded and updated, involving numerous improvements.
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