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