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Analysis of Matrix Calculations 2 - NMNM332

Title:	Analýza maticových výpočtů 2
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Additional information:	https://dl1.cuni.cz/course/view.php?id=9432

Guarantor:	doc. RNDr. Iveta Hnětynková, Ph.D.
Teacher(s):	doc. RNDr. Iveta Hnětynková, Ph.D.
Class:	M Bc. OM M Bc. OM > Zaměření NUMMOD M Bc. OM > Povinně volitelné
Classification:	Mathematics > Numerical Analysis
Pre-requisite :	{Analýza maticových výpočtů 1}
In complex pre-requisite:	NMNM349

Opinion survey results Examination dates Noticeboard

Annotation -

The course extends the curriculum of NMNM331. Recommended for bachelor's program in General Mathematics, specialization Mathematical Modelling and Numerical Analysis.

Last update: G_M (16.05.2012)

Course completion requirements -

To finish the course successfully, it is required to pass the exam covering all presented topics, see "Requirements to the exam". It is probable that a large part of the exams or credits could take place in a distance form. It depends on a development of the situation and we will inform you about the changes immediately.

To complete successfully the laboratory part, a student has to participate actively at the exercises (both theoretical and practical in MATLAB).

Last update: Hnětynková Iveta, doc. RNDr., Ph.D. (15.02.2022)

Literature -

Duintjer Tebbens, J., Hnětynková, I., Plešinger, M., Strakoš, Z., Tichý, P., Analýza metod pro maticové výpočty I, Skripta MFF UK, 2011.

Drkošová, J., Strakoš, Z., Základy teorie citlivosti a numerické stability, Skripta FJFI ČVUT, 1995.

Watkins, D.S., Fundamentals of Matrix Computations, J. Wiley & Sons, New York, Second edition 2002, Third edition, 2010.

Last update: Hnětynková Iveta, doc. RNDr., Ph.D. (07.04.2015)

Teaching methods -

Lectures are held in a lecture hall. Practicals in computer laboratory where we regularly switch between solution of examples on the blackboard and in the Matlab programming enviroment.

In case of distance learning, the course will be held online on ZOOM platform.

Last update: Hnětynková Iveta, doc. RNDr., Ph.D. (26.02.2021)

Requirements to the exam -

The final exam has oral form and covers all material presented in lectures and practicals and assigned through MOODLE1 page of the course during the semester.

Depending on the situation, the exam can have a distance form (using ZOOM software etc.).

Last update: Hnětynková Iveta, doc. RNDr., Ph.D. (26.02.2021)

Syllabus -

1. Basic terminology and relations of the theory of sensitivity and numerical stability.

2. Sensitivity of matrix eigenvalues for general and normal matrices. Continuity and diferentiability, conditioning of a simple eigenvalue. Pseudospectrum.

3. Estimates of backward error for approximations of eigenvalues.

4. Estimates of backward error for approximate solutions of linear algebraic problems.

5. Inverse power method, simultanes subspace iterations.

6. QR algorithm (Francis algorithm) for the solution of full eigenvalue problem and computation of SVD.

7. Summary of related areas and topics.

Last update: Hnětynková Iveta, doc. RNDr., Ph.D. (26.02.2021)

Entry requirements -

Students are expected to have attended the course NMNM331.

Last update: G_M (16.05.2012)