Preface
Using This Guide
Organization of the Document
Related Products
Typographical Conventions
Introduction
What Is the Spline Toolbox?
New Features in Version 3.1.1
Smoothing Splines for Scattered Bivariate Data
splinetool Command History/M-File
Spline-Specific Zero Finder
Spline-Specific Minimum Finder
Other Enhancements
Splines in MATLAB
Expected Background
Technical Conventions
Examples
Tutorial
Some Simple Examples
Cubic Spline Interpolation
Periodic Data
Other End Conditions
General Spline Interpolation
Knot Choices
Smoothing
Least Squares
Using the Spline Fits
Vector-Valued Functions
Fitting Values at N-D Grid
Fitting Values at Scattered 2-D Sites
Splines: An Overview
Polynomials vs. Splines
ppform
B-form
Knot Multiplicity
B-Spline Properties
Constructive vs. Variational
Multivariate Splines
The ppform
Breaks
ppform
Construction
Use
The B-form
B-form
B-Splines
Knot Multiplicity
Choice of Knots
Splines
Construction
Example: A Spline Curve
Use
Tensor Product Splines
B-form
ppform
NURBS and Other Rational Splines
Rational Splines
Example: Circle
Example: Sphere
rsform
Use
The stform
stform
Use
Example: A Nonlinear ODE
Problem
Approximation Space
Discretization
Numerical Problem
Linearization
Linear System to Be Solved
Iteration
Example: Construction of the Chebyshev Spline
What Is a Chebyshev Spline?
Choice of Spline Space
Initial Guess
Remez Iteration
Example: Approximation by Tensor Product Splines
Choice of Sites and Knots
Least Squares Approximation as Function of y
Approximation to Coefficients as Functions of x
Switch in Order
Approximation to Coefficients as Functions of y
The Bivariate Approximation
Comparison and Extension
Functions - By Category
GUIs
Construction of Splines
Operators
Work with Breaks, Knots, and Sites
Customized Linear Equation Solver
Information About Splines and the Toolbox
Demonstrations
Utilities
Functions - Alphabetical List
Glossary
Introduction
List of Terms
Intervals
Vectors
Functions
Placeholder notation
Curves and surfaces vs. functions
Tensor products
Polynomials
Piecewise-polynomials
B-splines
Splines
Rational splines
Thin-plate splines
Interpolation
Schoenberg-Whitney Theorem
Least-squares approximation
Smoothing
Printable Documentation (PDF)
Product Page (Web)