README.md

Practical programming and numerical methods

Practical programming and numerical methods -- spring 2021. The folder "Exam" contains my solution to exam problem number 5: Adaptive 1D integrator with random nodes. The folder "Homeworks" containts solutions to (most) of problems listed below. The folder "Lectures" containts various bits from the lectures and should generally be ignored.

1. Interpolation
   1. Linear spline
   2. Quadratic spline
   3. Cubic spline
2. Linear equations
   1. QR-decomposition by modified Gram-Schmidt orthogonalization
   2. Matrix inverse by Gram-Schmidt QR factorization
   3. Operations count for QR-decomposition and comparison with GSL
3. Least squares
   1. Ordinary least-squares fit by QR-decomposition
   2. Uncertainties of the fitting coefficients
   3. Evaluation of the quality of the uncertainties on the fit coefficients
4. Matrix diagonalization
   1. Jacobi diagonalization with cyclic sweeps
   2. Quantum particle in a box
   3. Scaling, optimization, and comparison with GSL
5. Ordinary differential equations
   1. Embedded Runge-Kutta ODE integrator
   2. Store the path
   3. Newtonian gravitational three-body problem
6. Adaptive Integration
   1. Recursive adaptive integrator
   2. Open quadrature with Clenshaw–Curtis variable transformation
   3. Infinite limits
7. Monte Carlo integration
   1. Plain Monte Carlo integration
   2. Multidimensional Monte-Carlo integrator
   3. Recursive stratified sampling
8. Root Finding
   1. Newton's method with numerical Jacobian and back-tracking linesearch
   2. Bound states of hydrogen atom with shooting method for boundary value problems
   3. Better boundary condition for the hydrogen atom problem
9. Minimization
   1. Quasi-Newton method with numerical gradient, back-tracking linesearch, and rank-1 update
   2. Higgs discovery
   3. Implement the downhill simplex method
10. Artificial Neural Networks