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