## Foundations of Computational Mathematics, Minneapolis 2002The Foundations of Computational Mathematics meetings are a platform for cross-fertilization between numerical analysis, mathematics and computer science. This volume, first published in 2004, contains the plenary presentations, given by some of the leading authorities in the world, and topics surveyed range from optimization to computer algebra, image processing to differential equations, quantum complexity to geometry. The volume will be essential reading for all those wishing to be informed of the state-of-the-art in computational mathematics. |

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### Contents

Some Fundamental Issues | 1 |

Jacobi Sets | 37 |

Approximation of boundary element operators | 58 |

Quantum Complexity | 76 |

Straightline Programs | 96 |

Numerical Solution of Structured Problems | 137 |

Detecting Infeasibility | 157 |

Maple Packages and Java Applets | 193 |

### Common terms and phrases

adaptive methods applications approximation Besov spaces binary bits central path certificate of infeasibility Chow form classical cluster co-dimension coefficients complexity components compression convergence corresponding critical points defined degree bounded denotes deterministic differential dimension dimensional dual eigenvalue problem equation equidimensional variety error example exponential feasible solution Finite Element Methods geometric resolution given Hamiltonian Heintz IIP method information-based complexity input polynomials integration interior-point method Jacobi set Lie algebra linear algebra linear programming lower link Math matrix Morse functions multiplicity Newton's method norm Nullstellensatz numerical methods obtain operations orthogonal parameters partition pencil piecewise linear positive primal quantization quantum algorithms quantum computing qubit recursive satisfying sequence shadow iterates Sigma-Delta sip's smooth smooth functions sons(r sparse straight-line program strictly feasible strictly infeasible structure symmetric symplectic Theorem theory transformation triangular cells triangulation values variables vector fields Vessiot W2-matrix wavelet zero zero-dimensional

### Popular passages

Page 191 - Approximate Farkas lemmas and stopping rules for iterative infeasible-point algorithms for linear programming,