Introduction
|
Motivation and scope of this overview.
|
Polynomials vs. Splines
|
Rationale for the use of piecewise polynomials, also known as splines.
|
ppform
|
Formal description of the ppform.
|
B-form
|
Formal description of the B-form.
|
Knot Multiplicity
|
Discusses the interplay between knot multiplicity and smoothness of a spline in B-form.
|
B-Spline Properties
|
Lists the basic properties of a B-spline, including its associated dual functional.
|
Constructive vs. Variational
|
Relates and compares standard ways for constructing a spline satisfying certain conditions with the way splines occur naturally as constrained minimizers of certain functionals that measure the size of some derivative.
|
Multivariate Splines
|
Discusses the tensor product construct for using univariate approximation methods for multivariate gridded data, as well as the use of thin-plate splines for the fitting to scattered data.
|
Rational Splines
|
Description of rational splines and their rsforms.
|
