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Computational Mathematics (Numerical Differentiation and Integration,…

- - - - Pivoting strategy
        for stability reason
        
        Partial pivoting
        
        Total pivoting
      - Cholesky factorization
        for SPD matrices
      - Sparsity
      - Reordering strategy to
        Reduce the Fill-Ins
  - - - a parallel algorithm
    - - Not a parallel algorithm
    - - For all x0, {xk} converges to the exact solution x iff ‖T‖ < 1
      - Both Jacobi & Gauss-Seidel method converges if A is strictly diagonal dominant
      - If A is PD, relaxation method converges iff 0 < w < 2
      - If A is PD & tridiagonal, the best choice of w is given.
  - - - well / ill conditioned matrices
- - - - Runge's Phenomenon
      - Chebyshev Nodes
      - Stability analysis
    - - Discrete Fourier Series & FFT
      - Need enough points to avoid Aliasing