List of numerical analysis topics
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This is a list of numerical analysis topics, by Wikipedia page.
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General
- Kahan summation algorithm
- Iterative method
- Richardson extrapolation
- Evaluation of polynomials:
- Evaluation of special functions:
- Level set method
- Abramowitz and Stegun
- Curse of dimensionality
- Superconvergence
- Termination
Error
- Condition number
- Numerical stability
- Well-posed problem
- Significant figures
- Loss of significance
- Propagation of errors resulting from algebraic manipulations
- Precision (arithmetic)
- Hilbert matrix
- Floating point number
- Truncation
- Round-off error
- Discretization error
- Approximation error
Numerical linear algebra
- Sparse matrix
- Circulant matrix
- Strassen algorithm
- Solving a system of linear equations:
- Eigenvalue algorithms:
- Orthogonalization:
Interpolation
- Polynomial interpolation
- Linear interpolation
- Runge's phenomenon
- Vandermonde matrix
- Chebyshev nodes
- Lebesgue constant (interpolation)
- Different forms for the interpolant:
- Extensions to multiple dimensions:
- Hermite interpolation
- Birkhoff interpolation
- Spline interpolation
- SLERP
- Wavelet
- Inverse distance weighting
- Trigonometric interpolation
- Irrational base discrete weighted transform
- Extrapolation
- Regression analysis
- Approximation theory
Finding roots of equations
- Root-finding algorithm
- Bisection method
- False position method
- Newton's method
- Secant method
- Müller's method
- Inverse quadratic interpolation
- Brent's method
- Laguerre's method
- Shifting nth-root algorithm
- Wilkinson's polynomial
Optimization
- Optimization glossary
- Continuous optimization
- Linear programming (also treats integer programming)
- Quadratic programming
- Convex optimization
- Nonlinear programming
- Global optimization
- Discrete optimization:
- Combinatorial optimization
- Stochastic programming
- Dynamic programming
- Random optimization algorithms:
- Infinite-dimensional optimization
- No-free-lunch theorem, No-Free-Lunch theorems
- see also the section Monte Carlo method
Numerical integration
- Trapezium rule
- Simpson's rule
- Newton-Cotes formulas
- Gaussian quadrature
- Romberg's method
- Sparse grid
- Numerical differentiation
Numerical ordinary differential equations
Numerical ordinary differential equations — the numerical solution of ordinary differential equations (ODEs)
- Runge-Kutta methods — one of the two main classes of methods for initial value problems
- Midpoint method — a second-order method with two stages
- Multistep method — the other main class of methods for initial value problems
- Newmark-beta method — a method specifically designed for the solution of problems from classical physics
- Verlet integration — another method for problems from classical physics
- Symplectic integrators — methods for the solution of Hamilton's equations that preserve the symplectic structure
- Stiff equation — roughly, an ODE for which the unstable methods needs a very short step size, but stable methods do not.
- Shooting method — a method for the solution of boundary value problems
Numerical partial differential equations
Numerical partial differential equations — the numerical solution of partial differential equations (PDEs)
- Methods for the solution of PDEs:
- Finite difference method — based on approximating differential operators with difference operators
- Discrete Laplace operator — finite-difference approximation of the Laplace operator
- Crank-Nicolson method — second-order method for heat and related PDEs
- Finite element method, finite element analysis — based on a discretization of the space of solutions
- Spectral method — based on the Fourier transformation
- Boundary element method — based on transforming the PDE to an integral equation on the boundary of the domain
- Finite volume method — based on dividing the domain in many small domains; popular in computational fluid dynamics
- Discrete element method — a method in which the elements can move freely relative to each other
- Finite difference method — based on approximating differential operators with difference operators
- Techniques for improving these methods:
- Multigrid, multigrid method — uses a hierarchy of nested meshes to speed up the methods
- Domain decomposition method — divides the domain in a few subdomains and solves the PDE on these subdomains
- Adaptive mesh refinement — uses the computed solution to refine the mesh only where necessary
- Mimetic methods — methods that respect in some sense the structure of the original problem
Monte Carlo method
- Quasi-Monte Carlo method
- Markov chain Monte Carlo
- Box-Muller transformation
- Low-discrepancy sequence
- Also see the list of statistics topics
Applications
Software
- Libraries:
- Languages:
- Programs: