A Domain Decomposition Method for Computing Bivariate Spline Fits of Scattered Data

A domain decomposition method for solving large bivariate scattered data fitting problems with bivariate minimal energy, discrete least-squares, and penalized least-squares splines is described. The method is based on splitting the domain into smaller domains, solving the associated smaller fitting problems, and combining the coefficients to get a global fit. Explicit error bounds are established for how well our locally constructed spline fits approximate the global fits. Some numerical examples are given to illustrate the effectiveness of the method. §