List of numerical analysis topics

Table of contents

1 General 2 Finding roots of equations 3 Interpolation 4 Optimization 5 Numerical integration 6 Numerical ordinary differential equations 7 Matrix problems 8 Orthogonalization 9 Finite element method 10 Monte Carlo method 11 Applications 12 Software

General

• Condition number
• Numerical stability
• Well-posed problem
• Significant figure
• Loss of significance
• Propagation of errors resulting from algebraic manipulations
• Accuracy and precision, decimal precision, precision
• Hilbert matrix
• Floating point number
• Kahan summation algorithm
• Round-off error
• Discretization error
• Approximation error
• Iterative method
• Richardson extrapolation
• Horner scheme
• Generating trigonometric tables

• Root-finding algorithm, equation solving
• Bisection method
• False position method
• Newton's method
• Secant method
• Shifting nth-root algorithm
• Wilkinson's polynomial

• Polynomial interpolation
  • Linear interpolation
  • Newton polynomial
  • Lagrange polynomial
  • Runge's phenomenon
  • Bilinear interpolation
  • Trilinear interpolation
• Spline interpolation, spline
  • Linear spline
  • Quadratic spline
  • Cubic spline
    • Cubic Hermite spline, cubic Hermite curve
    • Natural cubic spline
  • Hermite spline
  • Cardinal spline
  • Kochanek-Bartels spline
  • Catmull-Rom spline
  • de Boor algorithm
  • Bézier spline
  • B-spline
  • Nonuniform rational B-spline (NURBS)
  • de Casteljau's algorithm
• Chebyshev nodes
• Wavelet
  • Continuous wavelet transform
• Fast Fourier transform
• Extrapolation
• Curve fitting

• Linear programming
  • Simplex algorithm
• Quadratic programming
• Nonlinear programming
  • Gradient descent
• Stochastic programming
• Dynamic programming
• Random optimization
  • Simulated annealing
  • Particle swarm optimization
  • Stochastic tunneling
• see also the section Monte Carlo method

• Quadrature
• Trapezium rule
• Simpson's rule
• Newton-Cotes formulas
• Gaussian quadrature
• Romberg's method
• Sparse grid

• Finite difference
• Runge-Kutta methods
• Shooting method
  • Illustration of the shooting method

• Elementary matrix transformations
• Gaussian elimination
• Eigenvalue algorithm
  • Inverse iteration
  • Rayleigh quotient iteration
  • QR algorithm

• Gram-Schmidt process
• Householder transformation

• Spectral method
  • Pseudo-spectral method
• Multigrid
• Domain decomposition method
• Finite volume method
• Discrete element method

• Quasi-Monte Carlo method
• Markov chain Monte Carlo
  • Metropolis-Hastings algorithm
  • Gibbs sampling

• Climate model
• Computational chemistry
• Computational fluid dynamics
• Computational physics
• Coupled cluster
• Density functional theory
• Self-consistent field method

• LabVIEW
• MATLAB
• Netlib
• Numeric Python
• Numerical Recipes
• GNU Octave
• Scilab
• SciPy
• R programming language
• Rlab