TY - BOOK ID - 77860503 TI - Radial basis functions PY - 2003 SN - 1107128005 1280432292 9786610432295 0511179049 0511040202 0511148941 0511326025 0511543247 0511051247 9780511040207 9780511543241 6610432295 9780511051241 0521633389 9780521633383 9781107128002 9781280432293 9780511179044 9780511148941 9780511326028 9780521101332 0521101336 PB - Cambridge Cambridge University Press DB - UniCat KW - Radial basis functions. KW - Basis functions, Radial KW - Functions, Radial basis KW - Radial basis function method KW - Approximation theory KW - Radial basis functions KW - 517.518.8 KW - 681.3*G12 KW - 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) KW - Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) KW - 517.518.8 Approximation of functions by polynomials and their generalizations KW - Approximation of functions by polynomials and their generalizations UR - https://www.unicat.be/uniCat?func=search&query=sysid:77860503 AB - In many areas of mathematics, science and engineering, from computer graphics to inverse methods to signal processing, it is necessary to estimate parameters, usually multidimensional, by approximation and interpolation. Radial basis functions are a powerful tool which work well in very general circumstances and so are becoming of widespread use as the limitations of other methods, such as least squares, polynomial interpolation or wavelet-based, become apparent. The author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence and provides a careful classification of the radial basis functions into types that have different convergence. A comprehensive bibliography rounds off what will prove a very valuable work. ER -