Numerical Analysis

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Numerical Analysis


Orthogonal Polynomials

Hermite Polynomials

Wikipedia page

Legendre Polynomials

Wikipedia page

Laguerre Polynomials

Wikipedia page

Nonlinear Equations

Continuation/Homotopy Methods

Reference Numerical Optimization by Nocedal and Wright (2006)
Also known as zero-path following.
If you want to solve \(\displaystyle r(x)=0\) when \(\displaystyle r(x)\) is difficult (i.e. has non-singular Jacobian) then you can use this method.
Define the Homotopy map
\(\displaystyle H(x, \lambda)=\lambda r(x) + (1-\lambda)(x-a)\)

Numerical Differentiation

See finite differencing

Numerical Integration

See Quadrature rules