مستخدم:Chaos/قائمة مواضيع التحليل العددي

من ويكيبيديا، الموسوعة الحرة

فهرست

[تحرير] تحليل عددي

This is a list of numerical analysis topics, by Wikipedia page.

[تحرير] مواضيع عامة

  • خوارزمية جمع كاهان Kahan summation algorithm
  • طريقة تكرارية Iterative method
  • استكمال ريتشاردسون Richardson extrapolation
  • تقدير كثيرات الحدود:
    • مخطط هورنر Horner scheme
    • خوارزمية كلينشاو Clenshaw algorithm
    • خوارزمية دي كاستيلجاو De Casteljau's algorithm
  • تقدير الدوال الخاصة:
    • توليد الدوال المثلثية Generating trigonometric tables
    • طرق حوسبة الجذور التربيعية Methods of computing square roots
    • خوارزمية الجذر النوني n-th root algorithm
    • CORDIC
    • تقريب لانكزوس Lanczos approximation
  • طريقة مجموعة المستوى Level set method
  • Abramowitz and Stegun
  • Curse of dimensionality
  • تقارب فائق Superconvergence
  • Termination
  • Discretization
    • Sequence transformations
  • Difference quotient

[تحرير] الخطأ

  • تقريب Approximation
  • عدد شرطي Condition number
  • إستقرار رقمي 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
  • Percent error

[تحرير] جبر خطي عددي

  • أنماط المصفوفات التي تظهر في التحليل العددي :
    • Sparse matrix
    • Circulant matrix
    • Pentadiagonal matrix
    • Triangular matrix
  • خوارزميات جداء المصفوفات:
    • Strassen algorithm
    • Coppersmith-Winograd algorithm
  • حل جملة معادلات خطية:
    • Gaussian elimination
    • LU decomposition
      • Crout matrix decomposition
    • Block LU decomposition
    • LDU decomposition
    • Cholesky decomposition
      • Minimum degree algorithm
      • Symbolic Cholesky decomposition
    • Conjugate gradient method
  • خوارزمية القيمة الخاصة Eigenvalue algorithm :
    • Power method
    • Inverse iteration
    • Rayleigh quotient iteration
    • Arnoldi iteration
    • QR algorithm
    • Divide-and-conquer eigenvalue algorithm
  • تعامد Orthogonalization :
    • Gram-Schmidt process
    • Householder transformation
    • Givens rotation
  • QR decomposition
  • Krylov subspace

[تحرير] استيفاء

Interpolation

  • Nearest Neighbor Interpolation
  • Polynomial interpolation
    • Linear interpolation
    • Runge's phenomenon
    • Vandermonde matrix
    • Chebyshev polynomials
    • 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
    • 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
    • See also: List of numerical computational geometry topics
  • Slerp
  • Wavelet
    • Continuous wavelet
      • Continuous wavelet transform
  • Inverse distance weighting
  • Trigonometric interpolation
    • Fast Fourier transform
      • Bluestein's FFT algorithm
      • Bruun's FFT algorithm
      • Cooley-Tukey FFT algorithm
      • Goertzel algorithm
      • Prime-factor FFT algorithm
      • Rader's FFT algorithm
    • Sigma approximation
  • Irrational base discrete weighted transform
  • Pareto interpolation
  • Extrapolation
  • Regression analysis
    • Isotonic regression
  • Approximation theory
    • Orders of approximation
    • Lebesgue's lemma
    • Curve fitting
    • Different approximations:
      • Linear approximation
      • Padé approximant
  • Curve-fitting compaction

[تحرير] إيجاد جذور معادلة خطية

  • 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
  • Lehmer-Schur algorithm
  • Wilkinson's polynomial

[تحرير] استمثال

  • مصطلحات:
    • Active set
    • Candidate solution
    • Global optimum and Local optimum
    • Maxima and minima
  • Continuous optimization
  • برمجة خطية (أيضا تتعامل مع البرمجة الصحيحة Integer Programming)
    • Simplex algorithm
    • Interior point method
      • Mehrotra predictor-corrector method
    • Mixed integer programming
    • Linear complementarity problem
  • Quadratic programming
    • Linear least squares
    • Frank-Wolfe algorithm
  • Convex optimization
  • Nonlinear programming
    • Descent direction
    • Linesearch
      • Backtracking linesearch
      • Wolfe conditions
    • Gradient descent
      • Stochastic gradient descent
    • Newton's method in optimization
    • BFGS method
    • Nelder-Mead method
    • Golden section search
    • Tabu search
    • Nonlinear least squares
      • Expectation-maximization algorithm
      • Gauss-Newton algorithm
      • Levenberg-Marquardt algorithm
  • Combinatorial optimization
  • Stochastic programming
  • Dynamic programming
    • Bellman equation
  • Global optimization:
    • BRST algorithm
    • MCS algorithm
  • Random optimization algorithms:
    • Simulated annealing
    • Evolutionary algorithm
      • Differential evolution
    • Genetic algorithm, genetic programming
    • Particle swarm optimization
      • RPSO
    • Stochastic tunneling
    • see also the section Monte Carlo method
  • Infinite-dimensional optimization
    • Optimal control
    • Shape optimization
  • Optimal substructure
  • Theoretical aspects:
    • Farkas's lemma
    • Karush-Kuhn-Tucker conditions
    • Lagrange multipliers
    • No-free-lunch theorem, No-Free-Lunch theorems
  • تطبيقات:
    • Automatic label placement
    • Cutting stock problem
    • Expenditure minimization problem
    • Inventory control problem
    • Job-shop problem
    • Multidisciplinary design optimization
    • Paper bag problem

[تحرير] تكامل عددي

Numerical integration

  • Trapezium rule
  • Simpson's rule
  • Newton-Cotes formulas
  • Gaussian quadrature
  • Romberg's method
  • Sparse grid
  • Numerical differentiation
  • Euler-Maclaurin formula

[تحرير] معادلات تفاضلية نظامية عددية

معادلات تفاضلية نظامية عددية — الحل العددي للمعادلات التفاضلية النظامية (ODEs)

  • Euler integration — the most basic method for solving an ODE
  • 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
  • Geometric integrator — a method that preserves some geometric structure of the equation
    • Symplectic integrator — a method for the solution of Hamilton's equations that preserves 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

[تحرير] معادلات تفاضلية جزئية عددية

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
      • Galerkin method — a finite element method in which the residual is orthogonal to the finite element space
      • Rayleigh-Ritz method — a finite element method based on variational principles
      • Direct stiffness method — a particular implementation of the finite element method, often used in structural analysis
    • 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
    • Analytic element method — similar to the boundary element method, but the integral equation is evaluated analytically
    • 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
  • Numerical diffusion — diffusion introduced by the numerical method, above to that which is naturally present
  • Numerical resistivity — the same, with resistivity instead of diffusion
  • Multiphysics — models consisting of various submodels with different physics

[تحرير] طريقة مونتي كارلو

  • متغيرات طريقة مونتي كارلو:
    • Direct simulation Monte Carlo
    • Quasi-Monte Carlo method
    • Markov chain Monte Carlo
      • Metropolis-Hastings algorithm
      • Gibbs sampling
    • Dynamic Monte Carlo method
  • Box-Muller transform
  • Low-discrepancy sequence
    • Constructions of low-discrepancy sequences
    • Illustration of a low-discrepancy sequence
  • Parallel tempering
  • Techniques for reducing the variance:
    • Control variate
    • Importance sampling
    • VEGAS algorithm
  • تطبيقات:
    • Metropolis light transport
    • Monte Carlo methods in finance
    • Quantum Monte Carlo
  • Also see the list of statistics topics

[تحرير] تطبيقات

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

[تحرير] برمجيات

  • See also: List of numerical analysis software
  • Libraries:
    • Basic Linear Algebra Subprograms
    • dnAnalytics
    • EISPACK
    • GNU Scientific Library
    • LAPACK
    • LINPACK
    • Netlib
    • Numerical Recipes
    • SciPy
  • لغات برمجة :
    • bc programming language
    • F programming language
    • Fortran
    • General Algebraic Modeling System
    • J programming language
    • Numerical Python
    • PDL
    • R programming language
  • برامج :
    • MATLAB
    • GNU Octave
    • Scilab
    • Rlab
    • TK Solver



[تحرير] مقالات تتطلب تصنيف

Courant–Friedrichs–Lewy condition -- Explicit and implicit methods -- Finite element method in structural mechanics -- MISER algorithm -- Newton fractal -- Pseudospectrum -- Uniform theory of diffraction -- Weak formulation -- Radial basis function -- OpenBUGS -- Particle filter -- Braess' paradox -- Convex analysis -- Corner solution -- Discrete optimization -- Goal programming -- Pareto analysis -- Pareto principle -- Partial evaluation -- Subderivative -- Trust region -- Utility maximization problem -- Branch and bound -- Cutting-plane method -- Delayed column generation -- Karmarkar's algorithm -- MTD-f -- Reactive search -- Effective fitness -- Evolution strategy -- Evolutionary art -- Gene expression programming -- Human-based genetic algorithm -- Interactive evolutionary computation -- Interactive genetic algorithm -- Learning classifier system -- Memetic algorithm -- Neuroevolution -- Bairstow's method -- Durand-Kerner method -- Splitting circle method --

  • Complex wavelet transform / Discrete wavelet transform
  • Greedy algorithm, Greedy randomized adaptive search procedure, Hill climbing, Local search (optimization), Random-restart hill climbing (currently more about discrete optimization, but may be expanded to cover continuous optimization)
  • MANIAC II (computer)
  • Operations research (what is the relation between OR and optimization?)
  • Secular equation / Secular function
  • Structural analysis (very applied)


  • Category:Numerical analysis
  • Category:Approximation theory
  • Category:FFT algorithms
  • Category:Interpolation
  • Category:Monte Carlo method
  • Category:Numerical software is excluded, because it is covered by List of numerical analysis software
  • Category:Numerical linear algebra
  • Category:Optimization
    • Category:Optimization algorithms
      • Category:Evolutionary algorithms
  • Category:Root-finding algorithms
  • Category:Splines


Category:Numerical software -- Category:Optimization software -- Category:Combinatorial optimization -- Category:Genetic algorithms -- Category:Genetic programming -- Category:Interactive evolutionary computation