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 
 GaussSeidel iteration 
 SOR 

Modern iterative techniques
 Conjugate gradient 
 Krylov subspace methods 
 Preconditioning 
 Multigrid 
Least Squares
 Discrete least squares
 Singular value decomposition 

 Continuous least squares 
 Orthogonal polynomials
 Legendre 
 Chebyshev 

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 

 Hermite interpolation 
 Cubic splines 
 BSplines 
 Bezier curves 
 Subdivision algorithms 
Fourier transform
 Trigonometric polymonials 
 FFT 
Wavelet
 Wavelet basics 
 Wavelet transforms 
Numerical Differentiation
Numerical Integration
 NewtonCotes: basic and composite rules
 multidimensional case 

 Romberg Integration 
 Gauss Quadrature
 multidimensional case 

 Adaptive Integration
 GaussKronrod 

Initial value problems
 First order systems of ODE 
 Taylor's methods 
 RungeKutta methods 
 Variable step strategy 
 RungeKuttaFehlberg method 
 Multistep methods 
 PredictorCorrector 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.
