## Acta Numerica 1998:Acta Numerica is an annual volume presenting substantive survey articles in numerical analysis and scientific computing. The subjects and authors are chosen by a distinguished international Editorial Board so as to report the most important and timely developments in the subject in a manner accessible to the wider community of professionals with an interest in scientific computing. |

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### Contents

Monte Carlo and quasiMonte Carlo methods | 1 |

Nonlinear approximation | 51 |

Relative perturbation results for matrix eigenvalues | 151 |

Stability for timedependent differential equations | 203 |

Direct search algorithms for optimization calculations | 287 |

Choice of norms for data fitting | 337 |

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### Common terms and phrases

apply approximation theory assume assumptions asymptotic stability basis Besov spaces bidiagonal calculated Carlo methods characterization Chebyshev computation consider convergence Corollary corresponding current simplex defined Demmel denote derivatives DeVore diagonal dimension eigenvalues Eisenstat and Ipsen elements equation example F(vm finite free knot given greedy algorithm implies interpolation spaces intervals iteration Kreiss Lemma line search linear approximation lp norms Math minimization step Monte Carlo Monte Carlo integration Monte Carlo methods n-term approximation nonlinear approximation nonlinear methods nonsingular norm objective function obtain optimization orthogonal orthonormal parameters Parseval's relation partition PDEs piecewise constant piecewise polynomials points problem Proof properties quadratic quadrature quasi-Monte Carlo quasi-Monte Carlo methods quasi-random sequences random relative bound relative error relative perturbation resolvent estimate satisfies Section simplex step singular values Sobolev Sobolev space solution spline target function technique Theorem tion transformation trust region vector of variables wavelet coefficients xk+l zero