Computing bivariate splines in scattered data fitting and the finite-element method

A number of useful bivariate spline methods are global in nature, i.e., all of the coefficients of an approximating spline must be computed at one time. Typically this involves solving a system of linear equations. Examples include several well-known methods for fitting scattered data, such as the minimal energy, least-squares, and penalized least-squares methods. Finite-element methods for solving boundary-value problems are also of this type. It is shown here that these types of globally-defined splines can be efficiently computed, provided we work with spline spaces with stable local minimal determining sets.

• Type: Journal
• Year: 2008
• Where: NA
• Authors: Larry L. Schumaker
• Keywords: Bivariate Spline Methods, Least-squares Methods, NA 2008, Well-known Methods