# 714-0782/01 – Numerical methods (NM)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 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 Czech Year of introduction 2015/2016 Year of cancellation 2019/2020 Intended for the faculties USP Intended for study types Bachelor
Instruction secured by
KUC14 prof. RNDr. Radek Kučera, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 2+2

### 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:

[1] QUARTERONI, S., SACCO, R., SALERI, F. Numerical Mathematics. 2. vyd. New York: Springer, 2007. ISBN 978-3-540-49809-4.

### Recommended literature:

[1] SÜLI, E., MAYERS, D., F. An Introduction to Numerical Analysis. Cambridge: University Press, 2003. ISBN 978-0521007948.

### 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.

### 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

Full-time form (validity from: 2015/2016 Winter semester, validity until: 2019/2020 Summer semester)
Min. number of points
Examination Examination 100  51
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2018/2019 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 2 Compulsory study plan
2017/2018 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 2 Compulsory study plan
2016/2017 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 2 Compulsory study plan
2015/2016 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner