## Reliable numerical computationPublished 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. |

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### 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 |

Copyright | |

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### Common terms and phrases

application approach approximation backward error BLAS Cholesky decomposition clustering column pivoting complete pivoting complex condition number constraints convergence corresponding defective matrix defined Demmel denote diagonal Dongarra Dooren Duff efficiency eigenvalue problem eigenvectors EISPACK elements error analysis error bounds estimate example floating-point FORTRAN function Gaussian elimination given ill-conditioned ill-posed problem implementation interpolation iterative refinement Jordan Kagstrom KKT system Lanczos algorithm least squares problems Lemma linear algebra linear equations linear systems LINPACK Math mathematical matrix memory method minimum-degree multiple node non-singular non-zero null space numerical analysis numerical software numerically stable obtained optimization orthogonal Paige parallel parameters performed polynomial processors QR decomposition QR factorization quadratic programming rank residuals Ritz values rounding errors Schur complement Section semi-definite sequence single precision singular value solving sparse sparse matrix step structure symmetric techniques Theorem tion transformations updating variables vector zero