Numerical Analysis: Difference between revisions
No edit summary |
|||
| (3 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
Numerical Analysis | Numerical Analysis | ||
==Orthogonal Polynomials== | |||
===Hermite Polynomials=== | |||
{{main | Wikipedia: Hermite polynomials}} | |||
===Legendre Polynomials=== | |||
{{main | Wikipedia: Legendre polynomials}} | |||
===Laguerre Polynomials=== | |||
{{main | Wikipedia: Laguerre polynomials}} | |||
==Nonlinear Equations== | ==Nonlinear Equations== | ||
| Line 8: | Line 19: | ||
Define the Homotopy map<br> | Define the Homotopy map<br> | ||
<math>H(x, \lambda)=\lambda r(x) + (1-\lambda)(x-a)</math> | <math>H(x, \lambda)=\lambda r(x) + (1-\lambda)(x-a)</math> | ||
==Numerical Differentiation== | |||
See finite differencing | |||
==Numerical Integration== | |||
See Quadrature rules | |||
==Function Approximation== | |||
===Radial Basis Functions (RBF)=== | |||
See [http://num.math.uni-goettingen.de/schaback/teaching/sc.pdf A Practical Guide to Radial Basis Functions].<br> | |||
Radial Basis Functions are functions which are only dependent on the radius of the input: <math>\mathbf{\phi}(\mathbf{x}) = \phi(\Vert x\Vert)</math> | |||