## Advances in Numerical Analysis: Wavelets, subdivision algorithms, and radial basis functionsThe aim of this volume is to present research workers and graduate students with a state-of-the-art survey of some of the most active areas of numerical analysis. This, and a companion volume, arise from a Summer School intended to cover recent trends in the subject. The chapters are writtenby the main lecturers at the School, each of whom are internationally renowned experts in their respective fields.This volume covers wavelets from the point of view of spline theory, subdivision algorithms in geometric design and the theory of radial basis function approximation. |

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### Contents

Wavelets and Spline Interpolation | 1 |

Subdivision Schemes in ComputerAided Geometric | 36 |

The Theory of Radial Basis Function Approximation | 105 |

Copyright | |

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### Common terms and phrases

absolutely convergent absolutely integrable algorithm applied B-spline bounded Buhmann C.K. Chui cardinal function characteristic polynomial coefficients compact support compactly Computer constant multiple continuous control points convergent subdivision scheme converges uniformly Corollary cubic data points decomposition deduce defined definition derivatives of degree eigenvalues equation exists finite grid follows formula Fourier transform function f Further Gaussian given Hence implies inequality infinite initial data integer interpolation points interpolatory subdivision scheme inverse multiquadric Lemma limit function linear polynomial Lipschitz continuous magnitude matrix masks multiquadric radial functions multiresolution analysis multivariate nonnegative nonsingularity nonzero order of convergence orthogonal orthonormal wavelet parameters polynomial of degree polynomial reproduction property radial basis function regular grid relation result right hand side satisfy the conditions sequence smoothness space subspaces supp(a Theorem 3.4 thin plate spline tion two-scale symbol uniform convergence uniformly convergent subdivision uniformly to zero values vector well-defined