| Spline Toolbox |
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- Using This Guide
- Organization of the Document
- Related Products
- Typographical Conventions
- 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
- 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
- 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
| | Preface | |