## Foundations of Computational Mathematics, Santander 2005, Volume 13This volume is a collection of articles based on the plenary talks presented at the 2005 meeting in Santander of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to non-experts who wish to gain some insight into the state of the art in this active and significant field. |

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### Contents

Section 1 | 36 |

Section 2 | 72 |

Section 3 | 73 |

Section 4 | 106 |

Section 5 | 143 |

Section 6 | 162 |

Section 7 | 179 |

Section 8 | 181 |

Section 12 | 201 |

Section 13 | 202 |

Section 14 | 208 |

Section 15 | 223 |

Section 16 | 230 |

Section 17 | 246 |

Section 18 | 251 |

Section 19 | 255 |

Section 9 | 187 |

Section 10 | 198 |

Section 11 | 199 |

Section 20 | 274 |

Section 21 | 343 |

Section 22 | 371 |

### Common terms and phrases

accurately evaluable algebraic apply approximation arithmetic Banach space black-box bound coeﬃcients component computational condition number Conjecture conservation consider constant convergence convex curse of dimensionality cusp cusp neighborhood decomposition deﬁned Deﬁnition Demmel denote diﬀerence dimension dimensionality discrete dominant terms eﬃcient eigenvalues Euclidean example ﬁnd ﬁnite element ﬁxed function Gaussian elimination Gaussian perturbations Geometry graph Greedy Algorithm Griebel group action Hamiltonian Heintz high-dimensional Hilbert space homogeneous horoballs hyperbolic 3-manifolds inﬁnite input irreducible iteration Lemma linear programming Math Mathematics matrix mesh method node nonlinear nonsmooth norm operations optimization output parameter Pardo partial diﬀerential equations problem proof properties random satisﬁes scheme Schršodinger equation Section Shub SIAM simplex simplex algorithm Smale smoothed analysis smoothed complexity solution solving sparse grid Spielman subspace suﬃcient symmetric symplectic Temlyakov Teng tensor product Theorem theory tion variables vector Zariski open zero