Numerical Analysis Tags

Numerical Analysis Tags

Error analysis

  • Round-off errors and computer arithmetic
  • Algorithms and convergence

Solutions of equations in one variable

  • Bisection method
  • Fixed-point iteration
  • Newton's method
  • Error analysis for iterative methods
  • Accelerating convergence
  • Zeros of polynomials and Müller's method

Polynomial approximation

  • Polynomial interpolation
  • Lagrange polynomials
  • Neville's method
  • Divided differences
  • Hermite interpolation

Polynomial approximation and splines

  • Linear splines
  • Quadratic splines
  • Cubic splines
  • B splines

Numerical differentiation

  • Numerical differentiation
  • Richardson extrapolation

Numerical integration

  • Trapezoid rule
  • Simpson's rule
  • Romberg integration
  • Adaptive quadrature methods
  • Gaussian quadrature
  • Multiple integrals

Initial-value problems for ordinary differential equations

  • Euler's method
  • Higher-order Taylor methods
  • Runge-Kutta methods
  • Error control
  • Runge-Kutta-Fehlberg method
  • Multistep Methods
  • Variable step-size multistep methods
  • Extrapolation methods
  • Higher-order equations and systems of differential equations
  • Stability
  • Stiff differential equations

Direct methods for solving linear systems

  • Pivoting strategies
  • Matrix inversion
  • Matrix factorization
  • Special types of matrices

++.Iterative techniques in matrix algebraI

  • The Jacobi and Gauss-Siedel iterative techniques
  • Relaxation techniques for solving linear systems
  • Error bounds and iterative refinement
  • Conjugate gradient method

Approximation theory

  • Discrete Least Squares Approximation
  • Orthogonal Polynomials and Least Squares Approximation
  • Chebyshev Polynomials and Economization of Power Series
  • Rational Function Approximation
  • Trigonometric Polynomial Approximation
  • Fast Fourier Transforms

Approximating eigenvalues

  • Orthogonal matrices and similarity transformations
  • Power method
  • Householder's method
  • QR algorithm
  • Singular value decomposition

Numerical solutions of nonlinear systems of equations

  • Fixed points for functions of several variables
  • Newton's methods
  • Quasi-Newton nethods
  • Steepest descent techniques
  • Homotopy and continuation methods

Boundary-value problems for ordinary differential equations

  • Linear shooting method
  • Shooting method for nonlinear problems
  • Finite-difference methods for linear problems
  • Finite-difference methods for nonlinear problems
  • Rayleigh-Ritz method

Numerical solutions to partial differential equations

  • Elliptical partial differential equations
  • Parabolic partial differential equations
  • Hyperbolic partial differential equations
  • Finite-element method
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