## Acta Numerica 2004:Acta Numerica surveys annually the most important developments in numerical mathematics and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important and timely developments in a manner accessible to the wider community of professionals with an interest in scientific computing. Acta Numerica volumes have proved to be a valuable tool not only for researchers and professionals wishing to develop their understanding of numerical techniques and algorithms and follow new developments, but also as an advanced teaching aid at colleges and universities. Many of the original articles have been used as the prime resource for graduate courses. This particular volume was originally published in 2004. |

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### Contents

The calculation of linear least squares problems | 1 |

Acta Numerica 2004 | 13 |

The numerical analysis of functional integral | 55 |

Sparse grids | 147 |

Complete search in continuous global optimization | 271 |

Multiscale computational modelling of the heart | 371 |

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adaptive algorithm Anal analysis Appl applications approach approximation basis functions bidiagonal branch and bound Brownian bridge Brunner Bungartz collocation methods collocation solution Comput constraints convergence convex corresponding curse of dimensionality defined delay differential equations delay VIE derivatives dimensionality dimensions discretization energy norm error example feasible point Figure finite element function value functional differential equations functional equations given global minimizer global optimization global optimization problems Golub grid points Griebel hierarchical Householder transformations integro-differential equations interpolation interval Iserles iterated kernels least squares problems Lemma linear least squares Math Mathematics matrix mesh Neumaier nonlinear obtain orthogonal parameters PDEs piecewise linear polynomial programming Proof proportional delays QR decomposition QR factorization quadratic quadrature reduced respect Section semilinear SIAM singular values solvers solving sparse grid sparse grid spaces subproblem subspace superconvergence techniques tensor product Theorem tion variables vector Volterra integral equations wavelets Zennaro