COURSE CONTENT:
Errors in numerical computing, floatingpoint number system and arithmetics. Evaluation of polynomials and their derivatives, Horner algorithm. Threeterm recurrence relations: properties and application to summation of series, Miller's algorithm. Some results from mathematical analysis. Polynomial interpolation: Lagrange and barycentric form. Newton's form of interpolation polynomial and the error estimate. Approximations of functions: L2 and maxnorm, vector and unitary spaces, orthonormal basis. Minimal distance and abstract problem of best approximation. Applications: Chebishev and Fourier approximation, discrete approximation. Numerical differentiation, Richardson extrapolation. Numerical integration (basic and extended formulas). Basics of numerical linear algebra (systems of linear equations, matrix condition number).
LEARNING OUTCOMES:
Students will be able to:
explain floatingpoint number system, explain and compare rounding vs. cutoff error.
evaluate polynomials, calculate sum of series of functions and identify possible numerical problems.
approximately solve nonlinear equations in one unknown.
approximate functions by applying the least squares method.
numerically evaluate derivative and integral of function and estimate the associated error.
EXAMINATION METHODS:
Written and oral exam.
