Preface (Spline Toolbox)

Spline Toolbox

Using This Guide

Organization of the Document

The main body of this guide comprises three chapters, and these are preceded by the Preface. Here, in tabular form, are the high points.

Chapter
Description

Chapter 1, Introduction
Introduces the Spline Toolbox, and explains the background of a typical person for whom it is intended. This chapter also explains technical conventions used in the book, and lists features that are new in Version 3.1.

Chapter 2, Tutorial
Some Simple Examples provides specific examples illustrating simple uses of the toolbox commands.
Splines: An Overview provides an overview of splines and spline approximation methods.
The ppform and The B-form offer detailed descriptions of the two basic ways used in the toolbox to describe a piecewise-polynomial (also known as a spline).
Tensor Product Splines concerns the use made in this toolbox of tensor products for multivariate work.
``NURBs and Other Rational Splines'' on page 2-36 discusses the use of the B-form and the ppform to describe rational splines.
``The stform'' on page 2-42 explains the form used in the toolbox to describe functions that involve a weighted sum of scattered translates of a so-called basis function, such as the thin-plate spline.

The remaining sections are meant for users interested in developing their own spline commands. Three specific computational tasks are discussed in detail:
Construction of the Chebyshev spline. See Example: Construction of the Chebyshev Spline.

Approximate solution of a nonlinear ordinary differential equation boundary value problem with a boundary layer. See Example: A Nonlinear ODE.

The use of univariate vector-valued splines in the construction and use of approximations to multivariate gridded data. See Example: Approximation by Tensor Product Splines.

Chapter 3, Reference
Begins with an ordered tabulation of the commands in this toolbox, followed by reference pages for those commands.

Glossary
Provides a briefing on the basic technical terms and concepts used in this guide.

Chapter	Description
Chapter 1, Introduction	Introduces the Spline Toolbox, and explains the background of a typical person for whom it is intended. This chapter also explains technical conventions used in the book, and lists features that are new in Version 3.1.
Chapter 2, Tutorial	Some Simple Examples provides specific examples illustrating simple uses of the toolbox commands. Splines: An Overview provides an overview of splines and spline approximation methods. The ppform and The B-form offer detailed descriptions of the two basic ways used in the toolbox to describe a piecewise-polynomial (also known as a spline). Tensor Product Splines concerns the use made in this toolbox of tensor products for multivariate work. ``NURBs and Other Rational Splines'' on page 2-36 discusses the use of the B-form and the ppform to describe rational splines. ``The stform'' on page 2-42 explains the form used in the toolbox to describe functions that involve a weighted sum of scattered translates of a so-called basis function, such as the thin-plate spline.
	The remaining sections are meant for users interested in developing their own spline commands. Three specific computational tasks are discussed in detail: Construction of the Chebyshev spline. See Example: Construction of the Chebyshev Spline. Approximate solution of a nonlinear ordinary differential equation boundary value problem with a boundary layer. See Example: A Nonlinear ODE. The use of univariate vector-valued splines in the construction and use of approximations to multivariate gridded data. See Example: Approximation by Tensor Product Splines.
Chapter 3, Reference	Begins with an ordered tabulation of the commands in this toolbox, followed by reference pages for those commands.
Glossary	Provides a briefing on the basic technical terms and concepts used in this guide.

Preface Related Products