Numerical Analysis: Difference between revisions
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==Orthogonal Polynomials== | ==Orthogonal Polynomials== | ||
===Hermite Polynomials=== | ===Hermite Polynomials=== | ||
{{main | Wikipedia: Hermite polynomials}} | |||
===Legendre Polynomials=== | ===Legendre Polynomials=== | ||
{{main | Wikipedia: Legendre polynomials}} | |||
===Laguerre Polynomials=== | ===Laguerre Polynomials=== | ||
{{main | Wikipedia: Laguerre polynomials}} | |||
==Nonlinear Equations== | ==Nonlinear Equations== | ||
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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> | |||