Numerical methods: task solving on the computer. The problem and source of numerical errors. Basic criteria in numerical analysis (conditioning) and numerical algorithms (error, complexity, stability, correctness).
Systems of linear equations and direct methods of solving them.
LU, Cholesky-Banachiewicz and QR decomposition.
Iterative methods of solving large systems of linear equations. Sparse matrices.
CG, GMRES, Jacobi, Gauss-Seidel and Richardson method. Their convergence and implementation.
Systems of nonlinear equations. Banach method.
Newton's, secant and Broyden's method. Convergence theorems. Stop criteria. Parallel computing.
Lagrange and Hermite polynomial interpolation.
Trigonometric and spline interpolation. Interpolation error. Horner's algorithm.
Mean-square approximation. Regular least squares problem.
Orthogonal polynomials. Uniform approximation by polynomials. FFT.
Quadratures. Truncation error. Rectangle, trapezoidal and Simpson's rule. Gaussian quadrature.
The approximate solution of differential equations. Monte Carlo methods.
Computer lab - mathematical packages: Octave, Matlab, R, Mathematica.
Computer lab - problem-solving on computers: Octave, Matlab, R, Mathematica.
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