SubjectsSubjects(version: 920)
Course, academic year 2022/2023
   Login via CAS
Fundamentals of Numerical Linear Algebra - NMMB203
Title: Základy numerické lineární algebry
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Is provided by: NMNM201
Guarantor: prof. RNDr. Vít Dolejší, Ph.D., DSc.
prof. Ing. Miroslav Tůma, CSc.
Class: M Bc. MMIB > Povinné
M Bc. MMIT > Povinné
Classification: Mathematics > Numerical Analysis
Interchangeability : NMNM201
In complex pre-requisite: NMNM331
Annotation -
Last update: T_KA (29.04.2015)
The first course of numerical linear algebra for students of MMIB.
Aim of the course -
Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (08.06.2015)

To give a basic knowledge in numerical linear algebra.

Course completion requirements - Czech
Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (24.09.2018)

Požadavky k zápočtu:

na cvičeních studenti dostanou postupně 3 úlohy, které řeší doma
nejpozději další týden před začátkem svého cvičení vyřešenou úlohu odevzdají (elektronicky či na papíře)
cvičícímu

za každou úlohu mohou získat 0 až 6 bodů
k udělení zápočtu je třeba získat alespoň 2/3 bodů, tedy 12.

„povaha kontroly studia předmětu“ vylučuje opakování této kontroly, POS, čl. 8, odst. 2

Literature -
Last update: prof. Ing. Miroslav Tůma, CSc. (09.10.2017)

Anne Greenbaum and Timothy P. Chartier: Numerical Methods: Design, Analysis and Computer Implementation of Algorithms, Princeton Universtity Press, 2012

A. Quarteroni and R. Sacco and F. Saleri: Numerical mathematics, Springer-Verlag, 2000

D. S. Watkins: Fundamentals of Matrix Computations, Willey Interscience, New Yourk, 2010 (third edition)

Tebbens, Hnětynková, Plešinger, Strakoš, Tichý: Analýza metod pro maticové výpočty - Základní metody, Skriptum MFF UK

Anne Greenbaum and Timothy P. Chartier: Numerical Methods: Design, Analysis and Computer Implementation of Algorithms, Princeton Universtity Press, 2012

Teaching methods -
Last update: prof. Ing. Miroslav Tůma, CSc. (09.10.2017)

Lectures and practicals in a lecture hall.

Requirements to the exam -
Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (08.06.2015)

Examination according to the syllabus.

Syllabus -
Last update: prof. Ing. Miroslav Tůma, CSc. (09.10.2017)

1. Introduction. What is numerical mathematics.

2. Problem types and errors (forward, backward, residual). Distinguishing factorization and eigenvalue problems.

3. Schur theorem and its consequences.

4. Orthogonality. QR factorization. Time complexity of the QR factorization and its stability.

5. LU factorization and solving systems of linear equations. Growth of errors in solving systems of linear equations.

6. Singular value decomposition. Least-squares problems.

7. Iterative methods based on splittings. Power method for eigenvalue problems. Ideas behind Krylov space methods.

 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html