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Numerical Analysis Practice

Experiment 1 Linear Equations Solving

  1. Gauss elimination
  2. Cholesky Factorization
  3. CG and GMRES

Compare the error

Experiment 2 Non-linear Equations Solving

  1. Direct function construction
  2. Accelerations --- Steffensen
  3. Newton

Requirements: Error < 1e-7

Experiment 3 Eigenvalue Calculation

  1. Jacobi method
  2. QR method

Experiment 4 Interpolation

  1. Lagrange interpolation
  2. Piecewise linear interpolation
  3. Cubic spline interpolation

Experiment 5 Function Approximation

  1. Best square approximation
  2. Tchebychev series truncation
  3. Lagrange remainder minimization

Experiment 6 Numerical Integration

  1. 5-point-Gauss-Legendre
  2. Romberg, Error<1e-7

Experiment 7 ODE Numerical Solution

  1. Explicit Runge-Kutta in 4 orders (ode45 without 5-order correction)
  2. Implicit Runge-Kutta in 4 orders

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