Algorithms for Approximation: 2(Chapman Hall/CRC Mathematics Series)

This volume comprises the proceedings of the second Shrivenham conference on Algorithms for Approximation. The term 'approximation' here refers to 'the approximation of functions and data by similar functions', and leads to such topics as curve and surface fitting, spline and piecewise polynomial methods, finite element modelling, and computer-aided design. Applications are given to a wide variety of areas such as surveying, meteorology, radar antenna and acoustic array design, topography, engineering metrology, and CAD/CAM. Emphasis at the meeting was placed on the development of useful algorithms, and on practical applications in defence and industry. In addition, some 40 submitted papers were selected and presented on a multitude of topics such as multivariate interpolation, optimization methods, constrained problems, spline fitting, data modelling, and applications in microwave measurement, isotropic antennas, sound measurement, and digitized contours.

Table of Contents:
Part 1 Development of algorithms: spline approximation - constrained spline approximation of functions and data based on constrained knot removal, E.Arge et al, near real-time spline fitting of long sequences of uniformly spaced data, T.Anthony, an algorithm for knot location in bivariate least squares spline approximation, M.Bozzini and F.de Tisi, a knot placement strategy for least squares spline fitting based on the use of local polynomial approximations, M.G.Cox et al, an algorithm for nonlinear splines with non-negativity constraints, G.Opfer, spline curve fitting of digitized contours, C.Potier and C.Vercken, a B-spline approximation algorithm for quasi-interpolation or filtering, C.Rabut, on knots and nodes for spline interpolation, P.W.Smith - polynomial and piecewise polynomial approximation - a basis for certain spaces of multivariate polynomials and exponentials, W.Dahmen, monotone piecewise cubic data fitting, F.N.Fritsch, direct and converse results on simultaneous approximation by the method of Bermstein-Durrmeyer operators, M.Heilmann and M.W.Muller, orthogonality and approximation in a Sobolev space by A.Iserles et al, piecewise polynomial approximation of polynomial curves, M.A.Lachance, calculation of the energy of a piecewise polynomial surface, E.Quak and L.L.Schumaker; interpolation - radial basis function interpolation on an infinte regular grid, M.D.Buhmann and M.J.D.Powell, the Fourier operator of even order and site application to an extremum problem in interpolation, L.Brutman, on multivariate polynomial interpolation, N.Dyn and A.Ron, algorithms for the construction of data dependent triangulations, N.Dyn et al, algorithms for computing best parametric cubic interpolation, C.Rademacher and K. Scherer; smoothing and constraint methods - data fitting by penalized least squares, M.Von Golitschek and L.L.Schumaker, a semi-infinite programming algorithm for constrained best approximation, K.W.Bosworth, inference region for a method of local approximation by using the residuals, M.Bozzinio and L.Lenarduzzi; complex approximation. (Part contents)