Problematics of numerical computing . Sources and types of errors. Conditionality of problems and algorithms.
Methods for solving algebraic and transcendental equations. The bisection method, the iterative method for solving equations.
The Newton method, the Regula-Falsi (False-Position) method, the combined method.
Solving systems of linear equations. Direct solution methods. Iterative methods (the Jacobi method, the Seidel method). Matrix norms.
Interpolation and approximation of functions. Approximation – the least-square method. Lagrange interpolation polynomials.
Newton interpolation polynomials. Spline-function interpolation.
Numerical integration. Newton-Cotes quadrature formulas. Composed quadrature formulas. Error estimation.
The Richardson extrapolation.
Initial value problems for ordinary differential equations. One-step methods. The Euler method. Error estimation using the half-step method.
The Runge-Kutta methods. Estimation of the approximation error.
Processing statistical data sets with one argument. Characteristics of statistical data sets, processing extensive statistical data sets.
Parameter estimation for basic data sets. Basic data set, random sampling, point and interval parameter estimates of the basic data set.
The goodness of fit tests. The Pearson χ2 test of the goodness of fit. The one- sample Kolmogorov-Smirnov test. The two-sample Kolmogorov-Smirnov test.
Methods for solving algebraic and transcendental equations. The bisection method, the iterative method for solving equations.
The Newton method, the Regula-Falsi (False-Position) method, the combined method.
Solving systems of linear equations. Direct solution methods. Iterative methods (the Jacobi method, the Seidel method). Matrix norms.
Interpolation and approximation of functions. Approximation – the least-square method. Lagrange interpolation polynomials.
Newton interpolation polynomials. Spline-function interpolation.
Numerical integration. Newton-Cotes quadrature formulas. Composed quadrature formulas. Error estimation.
The Richardson extrapolation.
Initial value problems for ordinary differential equations. One-step methods. The Euler method. Error estimation using the half-step method.
The Runge-Kutta methods. Estimation of the approximation error.
Processing statistical data sets with one argument. Characteristics of statistical data sets, processing extensive statistical data sets.
Parameter estimation for basic data sets. Basic data set, random sampling, point and interval parameter estimates of the basic data set.
The goodness of fit tests. The Pearson χ2 test of the goodness of fit. The one- sample Kolmogorov-Smirnov test. The two-sample Kolmogorov-Smirnov test.