Reliable Numerical ComputationM. G. Cox, S. J. Hammarling Published to honor the late Jim Wilkinson, the respected pioneer in numerical analysis, this book includes contributions from his colleagues and collaborators, leading experts in their own right. The breadth of Wilkinson's research is reflected in the topics covered, which include linear algebra, error analysis and computer arithmetic algorithms, and mathematical software. An invaluable reference, the book is completely up-to-date with the latest developments on the Lanczos algorithm, QR-factorizations, error propagation models, parameter estimation problems, sparse systems, and shape-preserving splines. Reflecting the current growth and vitality of this field, the volume is an essential reference for all numerical analysts. |
Contents
The Lanczos algorithm for a pure imaginary Hermitian matrix | 25 |
Computational aspects of the Jordan canonical form | 57 |
Some aspects of generalized QR factorizations 73 | 73 |
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Common terms and phrases
algorithm analysis application approach approximation arithmetic associated assume block bound called Cholesky clustering column complex computed condition number consider constraints corresponding decomposition defined described diagonal direct discuss effect efficiency eigenvalues elements elimination equations error estimate example execution factorization function give given implementation involved iterative iterative refinement Jordan least linear algebra linear systems machine Math mathematical matrix mean memory method needed normal Note numerical obtained operations orthogonal parallel performed perturbation pivoting positive possible practice precision problem programming rank reduced references residuals Ritz satisfies shows similar single singular solution solving sparse squares stable standard step structure symmetric symmetric matrix Table techniques Theorem tion transformations triangular University upper values variables vector Wilkinson zero