## Average-Case Analysis of Numerical Problems, Issue 1733The average-case analysis of numerical problems is the counterpart of the more traditional worst-case approach. The analysis of average error and cost leads to new insight on numerical problems as well as to new algorithms. The book provides a survey of results that were mainly obtained during the last 10 years and also contains new results. The problems under consideration include approximation/optimal recovery and numerical integration of univariate and multivariate functions as well as zero-finding and global optimization. Background material, e.g. on reproducing kernel Hilbert spaces and random fields, is provided. |

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### Contents

I | 1 |

II | 3 |

III | 7 |

IV | 9 |

V | 11 |

VI | 12 |

VIII | 13 |

X | 15 |

LVII | 105 |

LVIII | 106 |

LIX | 108 |

LX | 110 |

LXII | 112 |

LXIII | 113 |

LXIV | 114 |

LXVI | 115 |

XIII | 16 |

XIV | 17 |

XV | 18 |

XVI | 19 |

XVII | 21 |

XVIII | 24 |

XX | 25 |

XXI | 26 |

XXII | 27 |

XXIII | 28 |

XXIV | 29 |

XXV | 31 |

XXVI | 33 |

XXVII | 39 |

XXVIII | 40 |

XXIX | 44 |

XXX | 46 |

XXXII | 47 |

XXXIII | 48 |

XXXIV | 49 |

XXXV | 55 |

XXXVII | 56 |

XXXVIII | 58 |

XXXIX | 59 |

XLI | 62 |

XLIII | 63 |

XLIV | 65 |

XLV | 67 |

XLVI | 68 |

XLVII | 72 |

XLVIII | 79 |

XLIX | 81 |

LI | 82 |

LII | 83 |

LIII | 87 |

LIV | 92 |

LV | 93 |

LVI | 97 |

LXVII | 116 |

LXVIII | 119 |

LXIX | 123 |

LXX | 126 |

LXXI | 127 |

LXXII | 133 |

LXXIII | 134 |

LXXIV | 135 |

LXXV | 139 |

LXXVI | 148 |

LXXVII | 150 |

LXXVIII | 155 |

LXXIX | 157 |

LXXX | 158 |

LXXXI | 161 |

LXXXII | 167 |

LXXXIII | 168 |

LXXXIV | 170 |

LXXXV | 175 |

LXXXVI | 178 |

LXXXVII | 183 |

LXXXVIII | 184 |

LXXXIX | 187 |

XCI | 190 |

XCII | 192 |

XCIII | 194 |

XCIV | 196 |

XCV | 199 |

XCVI | 206 |

XCVII | 209 |

XCVIII | 213 |

XCIX | 214 |

C | 220 |

CI | 227 |

CII | 245 |

249 | |

CIV | 253 |

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### Common terms and phrases

A'-spline algorithm adaptive methods App2 Astd asymptotically optimal average case analysis average case results average case setting average error Brownian Brownian bridge Brownian motion Ck(D coefficients conditions of order consider corresponding covariance kernel cubature defined denote density dP(f function f function values global optimization Hermite data Hilbert space Holder conditions integration and approximation integration problem interpolation kernel Hilbert spaces knots Lemma linear methods linear problems lower bound mean Gaussian measure methods Sn minimal errors nonnegative definite Notes and References Novak optimal methods order optimal polynomial proof Proposition Proposition 31 quadratic mean quadrature formulas random fields random function regular sequence reproducing kernel Hilbert respect Ritter Sacks-Ylvisaker conditions Section Smolyak spline spline algorithms stochastic process subspace tensor product upper bound varying cardinality Wasilkowski weight function Wiener measure Wiener sheet worst case setting Wozniakowski yields Ylvisaker conditions zero finding zero mean Gaussian zero mean measure

### References to this book

Monte Carlo and Quasi-Monte Carlo Methods 2006 Alexander Keller,Stefan Heinrich,Harald Niederreiter Limited preview - 2007 |