## Numerical Analysis 1997This book forms a valuable guide to the direction in which current numerical analysis research is heading. It will be of particular interest to graduate students and researchers concerned with the theoretical and practical issues associated with scientific computation. The main topics include ordinary and partial differential equations, fluid flow, optimization, linear algebra, and approximation theory. Two recurring themes are the need for adaptive and structure preserving numerical methods. The work presented here has a list of direct applications that include colliding black holes, molecular dynamics, blow-up problems, and card shuffling. |

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### Contents

Adaptive finite elements | 1 |

Symmetry based numerical methods | 16 |

On the local behavior of | 37 |

Stability of Householder QR factorization | 57 |

J E Flaherty R M Loy M Dindar M S Shephard B K Szymanski | 74 |

Block triangular orderings and factors for sparse matrices in LP | 91 |

Longtime step methods | 111 |

On the role of the left starting vector in the twosided | 124 |

Order barriers for symplectic multivalue methods | 133 |

A numerical analyst looks at the cutoff | 150 |

Finite volume schemes in multidimensions | 179 |

Trust region calculations revisited | 193 |

The search for a good basis | 212 |

The convergence of iterative | 230 |

List of Contributed Talks | 244 |

### Common terms and phrases

adaptive analysis applied approximation asymptotic backward error barrier basis bisection black hole block bound boundary calculation coefficients column pivoting compression computation conjugate gradient conjugate gradient method conservation laws convergence cutoff phenomenon defined Department of Mathematics diagonal dimension eigenvalues eigenvectors error estimates example Figure filter finite element method finite volume schemes follows function given GMRES imbalance implicit LU factors impulse method initial data integration interior point method invariant iteration Lanczos algorithm left starting vector Lemma linear systems load balancing LU factors Markov chain Math matrix mesh multi-value methods multistep methods non-zero nonlinear numerical method numerical solution one-leg methods optimal ordinary differential equation orthogonal parameter partial differential equations polynomial predictive balancing problem processor recursion riffle shuffle row-wise satisfies self-similar solution SIAM solve Sorensen sparsity spike step symmetry symplectic tetrahedron Theorem triangular trust region underlying one-step method University variables vertex wavelet zero