6 Approximation Methods

6.1 Local Approximation Methods

6.2 Ordinary Regression as Approximation

6.3 Orthogonal Polynomials

6.4 Least-Squares Orthogonal Polynomial Approximation

6.5 Uniform Approximation

6.6 Interpolation

6.7 Approximation through Interpolation and Regression

6.8 Piecewise Polynomial Interpolation

6.9 Splines

6.10 Examples

6.11 Shape-Preserving Approximation

6.12 Multidimensional Approximation

6.13 Finite Element Approximations

6.14 Neural Networks

6.15 Further Reading and Summary

6.16 Exercises