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. Title......Page 1 Copyright ......Page 2 PREFACE ......Page 3 PARTICIPANTS ......Page 4 BOOLEAN METHODS IN FOURIER APPROXIMATION ......Page 7 ILL-POSED PROBLEMS IN MULTIVARIATE APPROXIMATION by E.W. Cheney ......Page 19 ON MULTIVARIATE VERTEX SPLINES AND APPLICATIONS by Charles K. Chui and Mingjun Lai ......Page 25 ON THE THEORY AND APPLICATION OF EXPONENTIAL SPLINES by W.Dahmen and C.A. Micchelli ......Page 43 INTERPOLATION OF SCATTERED DATA BY RADIAL FUNCTIONS by N.Dyn ......Page 53 SHAPE PRESERVING SURFACE INTERPOLATION by F.Fontanella ......Page 69 RECENT ADVANCES IN THE APPROXIMATION OF SURFACES FROM SCATTERED DATA by R.Franke ......Page 85 METAHARMONIC SPLINES FOR SOLVING THE EXTERIOR DIRICHLET PROBLEM FOR THE HELMHOLTZ EQUATION by W.Freeden ......Page 105 APPROXIMATION BY HARMONIC FUNCTIONS by Werner Haussmann ......Page 117 A SHORT SURVEY ON CARDINAL INTERPOLATION BY BOX SPLINES by K. Jetter......Page 131 UNISOLVENT INTERPOLATION IN ]Rn AND THE SIMPLICIAL POLYNOMIAL FINITE ELEMENT METHOD by A.J.Y. Le Mehaute ......Page 147 ON INTERPOLATION SYSTEMS AND ?-REDUCIBLE INTERPOLATION PROBLEMS by J. Lorente and V. Ramirez ......Page 159 ATTENUATION FACTORS AND MULTIVARIATE PERIODIC SPLINE INTERPOLATION by H.G. ter Morsche ......Page 171 COORDINATE FREE SCATTERED DATA INTERPOLATION by G.M. Nielson ......Page 181 APPROXIMATION BY POSITIVE ELEMENTS OF SUBALGEBRAS OF REAL-VALUED FUNCTIONS by J.B. Prolla......Page 191 NUMERICAL GENERATION OF NESTED SERIES OF GENERAL TRIANGULAR GRIDS by M.-C.Rivara ......Page 199 COMPOSITE FINITE ELEMENTS OF CLASS C2 by P.Sablonniere ......Page 213 TRIANGULATION METHODS by L.L. Schumaker ......Page 225 CONSTRAINED SURFACE CONSTRUCTION by F.I.Utreras ......Page 239 CONSTRAINED SURFACE CONSTRUCTION by F.I.Utreras ......Page 239 POLYNOMIAL REPRODUCING FORMULAS AND THE COMMUTATOR OF A LOCALLY SUPPORTED SPLINE by J.D.Ward ......Page 261 ON INEQUALITIES ARISING FROM BEST LOCAL APPROXIMATIONS IN RECTANGLES by F.Zo......Page 271 A BIBLIOGRAPHY OF MULTIVARIATE APPROXIMATION by R.Franke and L.L. Schumaker ......Page 281
