Topics in Multivariate Approximation

Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing.

Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book.

This monograph will be of interest to mathematicians.

Inhalt

Preface

Participants

Boolean Methods in Fourier Approximation

Ill-Posed Problems in Multivariate Approximation

On Multivariate Vertex Splines and Applications

On the Theory and Application of Exponential Splines

Interpolation of Scattered Data by Radial Functions

Shape Preserving Surface Interpolation

Recent Advances in the Approximation of Surfaces from Scattered Data

Metaharmonic Splines for Solving the Exterior Dirichlet Problem for the Helmholtz Equation

Approximation by Harmonic Functions

A Short Survey on Cardinal Interpolation by Box Splines

Unisolvent Interpolation in IRn and the Simplicial Polynomial Finite Element Method

On Interpolation Systems and H-reducible Interpolation Problems

Attenuation Factors and Multivariate Periodic Spline Interpolation

Coordinate Free Scattered Data Interpolation

Approximation by Positive Elements of Subalgebras of Real-Valued Functions

Numerical Generation of Nested Series of General Triangular Grids

Composite Finite Elements of Class C2

Triangulation Methods

Constrained Surface Construction

Polynomial Reproducing Formulas and the Commutator of a Locally Supported Spline

On Inequalities Arising from Best Local Approximations in Rectangles

A Bibliography of Multivariate Approximation