Jmw150/Computational-Science

numerical analysis algorithms

A collection of algorithms

Solve elementary algebraic equations of one variable

	Python	C	tested	proven
Bisection	X
fixed point iteration	X
Newton's	X
Secant	X
False position	X
Steffensen's	X
Horner's	X
Muller's	X

Interpolation and polynomial approximation

	Python	C	tested	proven
Neville's iterated interpolation
Newton's Divided-Difference Formula
Hermite Interpolation	X
Natural Cubic Spline
Clamped Cubic Spline
Bezier Curve

Differentiation and Integration

	Python	C	tested	proven
Composite Simpson's rule
Romberg	X
Adaptive Quadrature
Simpson's Double Integral
Gaussian Double Integral
Gaussian Triple Integral

Ordinary Differential Equations

	Python	C	tested	proven
Euler's
Runge-Kutta order 4
Runge-Kutta-Fehlberg
Adams 4th Order Predictor Corrector
Adams Variable Step-Size Predictor Corrector
Extrapolation
Runge-Kutta Method for diff eq systems
Trapezoidal with Newton Iteration

boundary value problems for ordinary differential equations

	Python	C	tested	proven
Linear Shooting
Nonlinear Shooting With Newton's Method
Linear Finite-Difference
Nonlinear Finite Difference
Piecewise Linear Rayleigh-Ritz
Cubic Spline Rayleigh-Ritz

Partial differential equations

	Python	C	tested	proven
Poisson Equation Finite-Difference
Heat Equation Backward-Difference
Crank-Nicolson
Wave Equation Finite-Difference
Finite Element

solving linear systems

	Python	C	tested	proven
Gaussian Elimination with Backward Substitution
Gaussian Elimination with Partial Pivoting
Gaussian Elimination with Scaled Partial Pivoting
LU factorization
LDL^t factorization
Cholesky
Crout Factorization for Tridiagonal Linear Systems

matrix algebra

	Python	C	tested	proven
Jacobi Iterative	X
Gauss-Seidel Iterative	X
SOR
Iterative Refinement
Preconditioned Conjugate Gradient Method

eigenvalues

	Python	C	tested	proven
Power Method
Symmetric Power Method
Inverse Power Method
Wielandt Deflation
Householder's
QR
Singular Value Decomposition

approximation methods

	Python	C	tested	proven
Pade Rational Approximation
Chebyshev Rational Approximation
Fast Fourier Transform

nonlinear systems

	Python	C	tested	proven
Newton's Method for systems
Broyden
Steepest Descent
Continuation Algorithm

Probability distributions

	Python	C	tested	proven
Binomial
Geometric
Hypergeometric
Poisson
Negative binomial
Uniform
Normal
Exponential
Gamma chi-square
Beta

Statistical Learning Theory

Analytic Number Theory

	Python	C	tested	proven
Tau
Sigma
Phi
Mobius
Riemann Zeta