List of numerical analysis topics and K. 499: Difference between pages
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#REDIRECT [[String Quartet in D major] |
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This is a '''list of [[numerical analysis]] topics''', by Wikipedia page. |
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==General== |
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*[[Kahan summation algorithm]] |
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*[[Iterative method]] |
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*[[Richardson extrapolation]] |
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*Evaluation of polynomials: |
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**[[Horner scheme]] |
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**[[Clenshaw algorithm]] |
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**[[De Casteljau's algorithm]] |
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*Evaluation of special functions: |
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**[[Generating trigonometric tables]] |
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**[[n-th root algorithm]] |
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**[[CORDIC]] |
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**[[Lanczos approximation]] |
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*[[Level set method]] |
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*[[Abramowitz and Stegun]] |
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*[[Curse of dimensionality]] |
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*[[Superconvergence]] |
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*[[Termination]] |
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==Error== |
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*[[Condition number]] |
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*[[Numerical stability]] |
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*[[Well-posed problem]] |
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*[[Significant figures]] |
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*[[Loss of significance]] |
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*[[Propagation of errors resulting from algebraic manipulations]] |
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*[[Precision (arithmetic)]] |
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*[[Hilbert matrix]] |
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*[[Floating point number]] |
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*[[Truncation]] |
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*[[Round-off error]] |
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*[[Discretization error]] |
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*[[Approximation error]] |
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==Numerical linear algebra== |
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*[[Sparse matrix]] |
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*[[Circulant matrix]] |
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*[[Strassen algorithm]] |
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*Solving a [[system of linear equations]]: |
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**[[Gaussian elimination]] |
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**[[LU decomposition]] |
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***[[Crout matrix decomposition]] |
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**[[Block LU decomposition]] |
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**[[LDU decomposition]] |
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**[[Cholesky decomposition]] |
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***[[Minimum degree algorithm]] |
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***[[Symbolic Cholesky decomposition]] |
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**[[Conjugate gradient method]] |
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*[[Eigenvalue algorithm]]s: |
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**[[Power method]] |
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**[[Inverse iteration]] |
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**[[Rayleigh quotient iteration]] |
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**[[Arnoldi iteration]] |
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**[[QR algorithm]] |
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**[[Divide-and-conquer eigenvalue algorithm]] |
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*[[Orthogonalization]]: |
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**[[Gram-Schmidt process]] |
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**[[Householder transformation]] |
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**[[Givens rotation]] |
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==[[Interpolation]]== |
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*[[Polynomial interpolation]] |
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**[[Linear interpolation]] |
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**[[Runge's phenomenon]] |
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**[[Vandermonde matrix]] |
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**[[Chebyshev nodes]] |
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**[[Lebesgue constant (interpolation)]] |
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**Different forms for the interpolant: |
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***[[Newton polynomial]] |
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****[[Divided differences]] |
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***[[Lagrange polynomial]] |
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***[[Bernstein polynomial]] |
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**Extensions to multiple dimensions: |
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***[[Bilinear interpolation]] |
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***[[Trilinear interpolation]] |
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***[[Bicubic interpolation]] |
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**[[Hermite interpolation]] |
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**[[Birkhoff interpolation]] |
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*[[Spline interpolation]] |
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**[[spline (mathematics)|Spline]] |
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**[[Cubic Hermite spline]] |
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**[[Hermite spline]] |
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**[[Cardinal spline]] |
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**[[Kochanek-Bartels spline]] |
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**[[Catmull-Rom spline]] |
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**[[de Boor algorithm]] |
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**[[B-spline]] |
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***[[Truncated power function]] |
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**[[Nonuniform rational B-spline]] (NURBS) |
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**[[Bézier spline]] |
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***[[Bézier curve]] |
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***[[de Casteljau's algorithm]] |
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*[[SLERP]] |
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*[[Wavelet]] |
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**[[Continuous wavelet]] |
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***[[Continuous wavelet transform]] |
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*[[Inverse distance weighting]] |
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*[[Trigonometric interpolation]] |
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**[[Fast Fourier transform]] |
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*[[Irrational base discrete weighted transform]] |
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*[[Extrapolation]] |
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*[[Regression analysis]] |
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*[[Approximation theory]] |
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**[[Linear approximation]] |
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**[[Orders of approximation]] |
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==Finding roots of equations== |
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*[[Root-finding algorithm]] |
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*[[Bisection method]] |
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*[[False position method]] |
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*[[Newton's method]] |
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*[[Secant method]] |
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*[[Müller's method]] |
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*[[Inverse quadratic interpolation]] |
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*[[Brent's method]] |
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*[[Laguerre's method]] |
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*[[Shifting nth-root algorithm]] |
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*[[Wilkinson's polynomial]] |
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==[[Optimization (mathematics)|Optimization]]== |
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*[[Optimization glossary]] |
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*[[Continuous optimization]] |
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*[[Linear programming]] (also treats ''integer programming'') |
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**[[Simplex algorithm]] |
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**[[Interior point method]] |
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***[[Mehrotra predictor-corrector method]] |
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**[[Mixed integer programming]] |
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*[[Quadratic programming]] |
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**[[Linear least squares]] |
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*[[Convex optimization]] |
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*[[Nonlinear programming]] |
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**[[Descent direction]] |
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**[[Linesearch]] |
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***[[Backtracking linesearch]] |
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***[[Wolfe conditions]] |
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**[[Gradient descent]] |
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***[[Stochastic gradient descent]] |
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**[[Newton's method in optimization]] |
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**[[BFGS method]] |
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**[[Downhill simplex method]] |
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**[[Golden section search]] |
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**[[Tabu search]] |
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**Nonlinear [[least squares]] |
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***[[Expectation-maximization algorithm]] |
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***[[Gauss-Newton algorithm]] |
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***[[Levenberg-Marquardt algorithm]] |
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*[[Global optimization]] |
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*[[Discrete optimization]]: |
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**[[Branch and bound]] |
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**[[Cutting-plane method]] |
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**[[Delayed column generation]] |
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*[[Combinatorial optimization]] |
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*[[Stochastic programming]] |
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*[[Dynamic programming]] |
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*[[Random optimization]] algorithms: |
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**[[Simulated annealing]] |
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**[[Evolutionary algorithm]] |
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**[[Genetic algorithm]], [[genetic programming]] |
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**[[Particle swarm optimization]] |
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**[[Stochastic tunneling]] |
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*[[Infinite-dimensional optimization]] |
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**[[Shape optimization]] |
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*[[No-free-lunch theorem]], [[No-Free-Lunch theorems]] |
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*see also the section ''Monte Carlo method'' |
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==[[Numerical integration]]== |
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*[[Trapezium rule]] |
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*[[Simpson's rule]] |
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*[[Newton-Cotes formulas]] |
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*[[Gaussian quadrature]] |
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*[[Romberg's method]] |
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*[[Sparse grid]] |
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*[[Numerical differentiation]] |
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==Numerical ordinary differential equations== |
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[[Numerical ordinary differential equations]] — the numerical solution of ordinary differential equations (ODEs) |
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*[[Runge-Kutta methods]] — one of the two main classes of methods for initial value problems |
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**[[Midpoint method]] — a second-order method with two stages |
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*[[Multistep method]] — the other main class of methods for initial value problems |
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*[[Newmark-beta method]] — a method specifically designed for the solution of problems from classical physics |
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*[[Verlet integration]] — another method for problems from classical physics |
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*[[Symplectic integrator]]s — methods for the solution of Hamilton's equations that preserve the symplectic structure |
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*[[Stiff equation]] — roughly, an ODE for which the unstable methods needs a very short step size, but stable methods do not. |
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*[[Shooting method]] — a method for the solution of boundary value problems |
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**[[Illustration of the shooting method]] |
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==Numerical partial differential equations== |
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[[Numerical partial differential equations]] — the numerical solution of partial differential equations (PDEs) |
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*Methods for the solution of PDEs: |
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**[[Finite difference]] method — based on approximating differential operators with difference operators |
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***[[Discrete Laplace operator]] — finite-difference approximation of the Laplace operator |
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***[[Crank-Nicolson method]] — second-order method for heat and related PDEs |
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**[[Finite element method]], [[finite element analysis]] — based on a discretization of the space of solutions |
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**[[Spectral method]] — based on the Fourier transformation |
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***[[Pseudo-spectral method]] |
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**[[Boundary element method]] — based on transforming the PDE to an integral equation on the boundary of the domain |
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**[[Finite volume method]] — based on dividing the domain in many small domains; popular in computational fluid dynamics |
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**[[Discrete element method]] — a method in which the elements can move freely relative to each other |
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*Techniques for improving these methods: |
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**[[Multigrid]], [[multigrid method]] — uses a hierarchy of nested meshes to speed up the methods |
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**[[Domain decomposition method]] — divides the domain in a few subdomains and solves the PDE on these subdomains |
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**[[Adaptive mesh refinement]] — uses the computed solution to refine the mesh only where necessary |
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*[[Mimetic]] methods — methods that respect in some sense the structure of the original problem |
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==[[Monte Carlo method]]== |
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*[[Quasi-Monte Carlo method]] |
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*[[Markov chain Monte Carlo]] |
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**[[Metropolis-Hastings algorithm]] |
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**[[Gibbs sampling]] |
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*[[Box-Muller transformation]] |
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*[[Low-discrepancy sequence]] |
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**[[Constructions of low-discrepancy sequences]] |
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**[[Illustration of a low-discrepancy sequence]] |
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*Also see the [[list of statistics topics]] |
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==Applications== |
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*[[Climate model]] |
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*[[Computational chemistry]] |
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**[[Coupled cluster]] |
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**[[Density functional theory]] |
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**[[Self-consistent field method]] |
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*[[Computational fluid dynamics]] |
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**[[Large eddy simulation]] |
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**[[Smoothed particle hydrodynamics]] |
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*[[Computational physics]] |
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==Software== |
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*Libraries: |
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**[[Basic Linear Algebra Subprograms]] |
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**[[dnAnalytics]] |
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**[[EISPACK]] |
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**[[GNU Scientific Library]] |
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**[[LAPACK]] |
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**[[LINPACK]] |
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**[[Netlib]] |
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**[[Numerical Recipes]] |
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**[[SciPy]] |
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*Languages: |
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**[[bc programming language]] |
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**[[F programming language]] |
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**[[Fortran]] |
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**[[General Algebraic Modeling System]] |
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**[[J programming language]] |
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**[[Numerical Python]] |
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**[[PDL]] |
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**[[R programming language]] |
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*Programs: |
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**[[MATLAB]] |
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**[[GNU Octave]] |
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**[[Scilab]] |
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**[[Rlab]] |
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**[[TK Solver]] |
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[[Category:Numerical analysis|*]] |
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[[Category:Topic lists|Numerical analysis]] |
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[[Category:Math lists]] |
Revision as of 11:39, 11 December 2004
- REDIRECT [[String Quartet in D major]