Numerical Analysis Topics Outline
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Nonlinear Equations of one variable
Systems of nonlinear equations
Theory in solution of linear equations
 | Vector and matrix norms |
| Perturbation estimates |
Direct solution of linear equations
| Gaussian elimination |
| Pivoting |
| LU decomposition |
| Cholesky factorization |
| Banded and tridiagonal matrices |
| Iterative refinement |
| Cyclic reduction |
| Fast Poisson solver |
Classical Iterative techniques
| General iteration via matrix splitting |
| Classical Iterative schemes
 | Jacobi iteration |
| Gauss-Seidel iteration |
| SOR |
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Modern iterative techniques
| Conjugate gradient |
| Krylov subspace methods |
| Preconditioning |
| Multigrid |
Least Squares
| Discrete least squares
| Singular value decomposition |
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| Continuous least squares |
| Orthogonal polynomials
| Legendre |
| Chebyshev |
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Eigenvalue problems
| Power methods |
| Deflation |
| Householder reflection |
| Givens method |
| QR |
| Divide and conquer |
| Inverse iteration |
Polynomial Interpolation
| Lagrange interpolation
| basis form |
| divided difference forms |
| Higher dimensional case |
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| Hermite interpolation |
| Cubic splines |
| B-Splines |
| Bezier curves |
| Subdivision algorithms |
Fourier transform
| Trigonometric polymonials |
| FFT |
Wavelet
| Wavelet basics |
| Wavelet transforms |
Numerical Differentiation
Numerical Integration
| Newton-Cotes: basic and composite rules
| multidimensional case |
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| Romberg Integration |
| Gauss Quadrature
| multidimensional case |
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| Adaptive Integration
| Gauss-Kronrod |
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Initial value problems
| First order systems of ODE |
| Taylor's methods |
| Runge-Kutta methods |
| Variable step strategy |
| Runge-Kutta-Fehlberg method |
| Multistep methods |
| Predictor-Corrector pairs |
| Stiff equations |
Boundary value problems
Finite difference
| Derivation |
| Stability |
| Lax Theorem |
Finite elements
| Variational formulation |
| Convergence |
| Superconvergence |
Copyrighted by S.-Sum Chow
This page was last updated on 10/08/2002.
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