310-2420/02 – Numerical methods (NM)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 6 |
| Subject guarantor | prof. RNDr. Radek Kučera, Ph.D. | Subject version guarantor | prof. RNDr. Radek Kučera, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 2 | Semester | winter |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Students completing the course will be able to: recognize problems that can be solved numerically; chose a suitable numerical method; decide on the correctness of computed results and on its influence by rounding errors, discretization errors, or errors of another type; identify numerically stable and unstable calculations and characterize them by the condition number; analyze numerical algorithms from the point of view of computational complexities and storage requirements; use the Matlab language and the standard Matlab libraries; propose algorithmically correct implementations of basic numerical methods, write it in the Matlab language, debug and test
Teaching methods
Lectures
Individual consultations
Tutorials
Project work
Summary
The course is devoted to basic numerical methods of the linear algebra and the mathematical analysis.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Tests and credits.
Exercises: conditions for obtaining credit points (CP
- participation in exercises, 20% can be to apologize,
- completion of three written tests, 0-15 CP,
- completion of two programs, 5 CP.
Exam:
- written exam 0-60 CP, successful completion at least 25 CP,
- oral exam 0-20 CP, successful completion at least 5 CP.
E-learning
Other requirements
They are no other requests for students.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Disciplines of numerical mathematics: continuous and discrete problems, discretization order; sources of error, rounding error, computer epsilon; numerical stability.
2. Approximation and interpolation of functions: polynomial interpolation, interpolation error; least squares approximation; uniform approximation, Bernstein polynomials, spline functions; modeling curves and surfaces, Bezier curves.
3. Rootfinding for nonlinear functions: geometric approach to rootfinding; fixed-point iterations and fixed point theorem; fundamental theorem of algebra, separations and calculations of polynomial roots; Newton's method for nonlinear systems.
4. Numerical integration and derivation: numerical differentiation, Richardson extrapolation; numerical quadrature formulas, error estimation, step size control; Romberg method; Gauss formulas.
5. Numerical linear algebra: solving linear systems using LU decomposition variants, inverse matrix; eigenvalues and eigenvectors calculation, spectral decomposition; singular value decomposition, orthogonal factorization, pseudoinverse.
6. Iterative methods for solving linear systems: linear methods Jacobi, Gauss-Seidel, relaxation; nonlinear methods, steepest descent method, conjugate gradient method, preconditioning.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.