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Course, academic year 2017/2018
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Analysis of Matrix Calculations 2 - NMNM332
Czech title: Analýza maticových výpočtů 2
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2014
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: 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
Annotation -
Last update: G_M (16.05.2012)

The course extends the curriculum of NMNM331. Recommended for bachelor's program in General Mathematics, specialization Mathematical Modelling and Numerical Analysis.
Literature -
Last update: RNDr. Iveta Hnětynková, Ph.D. (07.04.2015)

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.

Teaching methods -
Last update: RNDr. Iveta Hnětynková, Ph.D. (07.04.2015)

Lectures are held in a lecture hall. Practicals in computer laboratory (Matlab enviroment).

Requirements to the exam -
Last update: G_M (27.04.2012)

Written and oral part of the exam reflect the content of the course.

Syllabus -
Last update: RNDr. Iveta Hnětynková, Ph.D. (01.02.2016)

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. QR algorithm (Francis algorithm) for the solution of the complete eigenvalue problem. Inverse power method, simultanes subspace iterations.

6. Summary of related areas and topics.

Entry requirements -
Last update: G_M (16.05.2012)

Students are expected to have attended the course NMNM331.

 
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