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.
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.