Tasks + solutions
- task 1: computer arithmetic, floats, kahan algorithm, partial sums, roundup errors
- task 2: interpolation, polynomial interpolation, Chebyshev nodes, Runge's phenomenon, splines
- task 3: singular value decomposition, sphere transformations, image compression
- task 4: singular value decomposition, latent semantic indexing, information retrieval, inverse document frequency, search engine
- task 5: non-linear equations, bisection, Newton method, secant method
- task 6: solving linear equation systems, Gauss-Jordan method, LU decomposition (factorization), circuit analysis (kirchhoff and nodal), graphs
- task 7: spectral decomposition, eigenvalues, power method, inverse power method
- task 8: page rank, vertex ranking
- task 9: qr decomposition, least squares approximation
- task 10: discrete fourier transformation (DFT), fast fourier transformation (FFT), signal processing
- task 11: pseudorandom number generators, mersenne twister, pcg64, randomness test, uniform distribution, Gauss distribution, Box-Muller random generator, Shapiro-Wilk test, Monte Carlo pi estimation
- task 12: ordinary differential equations (ODE), Taylor series method, initial-value problem, analytical vs numerical solutions, Euler's method, Runge-Kutta method of order 4, adaptive Runge-Kutta-Fehlberg method, numerical stability
- task 13: simulated annealing, travelling salesman problem, function minimizing