Model, methods, and theory for fitting scattered data

Author: Wu Zongmin
Publisher:
Publish Date: 2007-01-01
Features: This book is an introductory text on surfaces and multivariate function interpolation, approximation, and fitting in applied mathematics and computational mathematics. It derives the mathematical models and computational methods for scattered data fitting from various physical backgrounds and principles, followed by in-depth theoretical analysis. The book introduces general methods for fitting scattered multivariate data, including polynomial interpolation for scattered multivariate data, interpolation methods based on triangulation, Boole and Coons surfaces, Sibson method or natural neighbor method, Shepard method, Kriging method, thin plate spline method, radial basis function method, moving least squares method, implicit function spline method, and R-function method, among others. It also specially introduces the radial basis function method, which has gained increasing international attention in recent years and has numerous applications in the numerical solution of meshfree differential equations, along with its related theories. This book is suitable for graduate students in applied mathematics and computational mathematics, as well as for researchers and engineers in fields such as hydrogeology, prediction and forecasting, pattern recognition, and statistical learning as a reference. ... The book introduces general methods for data fitting while keeping up with the latest developments in this field internationally, particularly the radial basis function method, whose core contents include: polynomial interpolation for scattered multivariate data, interpolation methods based on triangulation, Boole and Coons surfaces, Sibson method, Shepard method, Kriging method, and so on.