Numerical Analysis

Orthogonal Polynomials

Hermite Polynomials

Legendre Polynomials

Laguerre Polynomials

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

Function Approximation

Radial Basis Functions (RBF)

See A Practical Guide to Radial Basis Functions.
Radial Basis Functions are functions which are only dependent on the radius of the input: \(\displaystyle \mathbf{\phi}(\mathbf{x}) = \phi(\Vert x\Vert)\)