List of numerical analysis topics and K. 499: Difference between pages

From Wikipedia, the free encyclopedia
(Difference between pages)
Content deleted Content added
 
Fix
 
Line 1: Line 1:
#REDIRECT [[String Quartet in D major]
This is a '''list of [[numerical analysis]] topics''', by Wikipedia page.

==General==

*[[Kahan summation algorithm]]
*[[Iterative method]]
*[[Richardson extrapolation]]
*Evaluation of polynomials:
**[[Horner scheme]]
**[[Clenshaw algorithm]]
**[[De Casteljau's algorithm]]
*Evaluation of special functions:
**[[Generating trigonometric tables]]
**[[n-th root algorithm]]
**[[CORDIC]]
**[[Lanczos approximation]]
*[[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]]:
**[[Gaussian elimination]]
**[[LU decomposition]]
***[[Crout matrix decomposition]]
**[[Block LU decomposition]]
**[[LDU decomposition]]
**[[Cholesky decomposition]]
***[[Minimum degree algorithm]]
***[[Symbolic Cholesky decomposition]]
**[[Conjugate gradient method]]
*[[Eigenvalue algorithm]]s:
**[[Power method]]
**[[Inverse iteration]]
**[[Rayleigh quotient iteration]]
**[[Arnoldi iteration]]
**[[QR algorithm]]
**[[Divide-and-conquer eigenvalue algorithm]]
*[[Orthogonalization]]:
**[[Gram-Schmidt process]]
**[[Householder transformation]]
**[[Givens rotation]]

==[[Interpolation]]==

*[[Polynomial interpolation]]
**[[Linear interpolation]]
**[[Runge's phenomenon]]
**[[Vandermonde matrix]]
**[[Chebyshev nodes]]
**[[Lebesgue constant (interpolation)]]
**Different forms for the interpolant:
***[[Newton polynomial]]
****[[Divided differences]]
***[[Lagrange polynomial]]
***[[Bernstein polynomial]]
**Extensions to multiple dimensions:
***[[Bilinear interpolation]]
***[[Trilinear interpolation]]
***[[Bicubic interpolation]]
**[[Hermite interpolation]]
**[[Birkhoff interpolation]]
*[[Spline interpolation]]
**[[spline (mathematics)|Spline]]
**[[Cubic Hermite spline]]
**[[Hermite spline]]
**[[Cardinal spline]]
**[[Kochanek-Bartels spline]]
**[[Catmull-Rom spline]]
**[[de Boor algorithm]]
**[[B-spline]]
***[[Truncated power function]]
**[[Nonuniform rational B-spline]] (NURBS)
**[[Bézier spline]]
***[[Bézier curve]]
***[[de Casteljau's algorithm]]
*[[SLERP]]
*[[Wavelet]]
**[[Continuous wavelet]]
***[[Continuous wavelet transform]]
*[[Inverse distance weighting]]
*[[Trigonometric interpolation]]
**[[Fast Fourier transform]]
*[[Irrational base discrete weighted transform]]
*[[Extrapolation]]
*[[Regression analysis]]
*[[Approximation theory]]
**[[Linear approximation]]
**[[Orders of approximation]]

==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 (mathematics)|Optimization]]==

*[[Optimization glossary]]
*[[Continuous optimization]]
*[[Linear programming]] (also treats ''integer programming'')
**[[Simplex algorithm]]
**[[Interior point method]]
***[[Mehrotra predictor-corrector method]]
**[[Mixed integer programming]]
*[[Quadratic programming]]
**[[Linear least squares]]
*[[Convex optimization]]
*[[Nonlinear programming]]
**[[Descent direction]]
**[[Linesearch]]
***[[Backtracking linesearch]]
***[[Wolfe conditions]]
**[[Gradient descent]]
***[[Stochastic gradient descent]]
**[[Newton's method in optimization]]
**[[BFGS method]]
**[[Downhill simplex method]]
**[[Golden section search]]
**[[Tabu search]]
**Nonlinear [[least squares]]
***[[Expectation-maximization algorithm]]
***[[Gauss-Newton algorithm]]
***[[Levenberg-Marquardt algorithm]]
*[[Global optimization]]
*[[Discrete optimization]]:
**[[Branch and bound]]
**[[Cutting-plane method]]
**[[Delayed column generation]]
*[[Combinatorial optimization]]
*[[Stochastic programming]]
*[[Dynamic programming]]
*[[Random optimization]] algorithms:
**[[Simulated annealing]]
**[[Evolutionary algorithm]]
**[[Genetic algorithm]], [[genetic programming]]
**[[Particle swarm optimization]]
**[[Stochastic tunneling]]
*[[Infinite-dimensional optimization]]
**[[Shape 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 integrator]]s — 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
**[[Illustration of the shooting method]]

==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
***[[Pseudo-spectral method]]
**[[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
*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]]
**[[Metropolis-Hastings algorithm]]
**[[Gibbs sampling]]
*[[Box-Muller transformation]]
*[[Low-discrepancy sequence]]
**[[Constructions of low-discrepancy sequences]]
**[[Illustration of a low-discrepancy sequence]]
*Also see the [[list of statistics topics]]

==Applications==

*[[Climate model]]
*[[Computational chemistry]]
**[[Coupled cluster]]
**[[Density functional theory]]
**[[Self-consistent field method]]
*[[Computational fluid dynamics]]
**[[Large eddy simulation]]
**[[Smoothed particle hydrodynamics]]
*[[Computational physics]]

==Software==

*Libraries:
**[[Basic Linear Algebra Subprograms]]
**[[dnAnalytics]]
**[[EISPACK]]
**[[GNU Scientific Library]]
**[[LAPACK]]
**[[LINPACK]]
**[[Netlib]]
**[[Numerical Recipes]]
**[[SciPy]]
*Languages:
**[[bc programming language]]
**[[F programming language]]
**[[Fortran]]
**[[General Algebraic Modeling System]]
**[[J programming language]]
**[[Numerical Python]]
**[[PDL]]
**[[R programming language]]
*Programs:
**[[MATLAB]]
**[[GNU Octave]]
**[[Scilab]]
**[[Rlab]]
**[[TK Solver]]

[[Category:Numerical analysis|*]]
[[Category:Topic lists|Numerical analysis]]
[[Category:Math lists]]

Revision as of 11:39, 11 December 2004

  1. REDIRECT [[String Quartet in D major]