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 MÃ¼ller'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