SubjectsSubjects(version: 901)
Course, academic year 2021/2022
  
Analysis of Matrix Calculations 1 - NMNM331
Title: Analýza maticových výpočtů 1
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information: https://dl2.cuni.cz/course/view.php?id=3458
Guarantor: doc. RNDr. Iveta Hnětynková, Ph.D.
Class: M Bc. OM
M Bc. OM > Zaměření NUMMOD
M Bc. OM > Povinně volitelné
M Bc. OM > Zaměření STOCH
Classification: Mathematics > Numerical Analysis
Pre-requisite : {NMNM201 v NMMB203}, {NMAG101 v NMAG111}, {NMAG102 v NMAG112}
Incompatibility : NNUM006
Interchangeability : NNUM006
Is incompatible with: NNUM006, NMNM931
Is pre-requisite for: NMNM349, NMNM351
Is interchangeable with: NMNM931, NNUM006
In complex pre-requisite: NMNM332
Annotation -
Last update: G_M (16.05.2012)
The course is devoted to fundamentals of numerical linear algebra, with the concetration on methods for solving linear algebraic equations, including least squares, and on eigenvalue problems. The course emphasizes formulation of questions, motivation and interconnections. Recommended for bachelor's program in General Mathematics, specializations Mathematical Modelling and Numerical Analysis, and Stochastics.
Course completion requirements -
Last update: doc. RNDr. Iveta Hnětynková, Ph.D. (07.09.2020)

To finish the course successfully, it is required to pass the exam covering all presented topics, see "Requirements to the exam".

To complete successfully the laboratory part of the exam, a student needs to get 3 point for the activity. A point can be obtain in two ways: by solving a given example on the blackboard, or by

completing a homework assigned during the semester. A list of homework (including the deadline for their online submission) will be available by the end of October.

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

Duintjer Tebbens, J., Hnětynková, I., Plešinger, M., Strakoš, Z., Tichý, P., Analýza metod pro maticové výpočty, základní metody, Matfzypress, Praha 2012.

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

Fiedler, M., Speciální matice a jejich užití. SNTL Praha, l980

Golub, G.H., Van Loan C.F., Matrix Computations (Third edition). J. Hopkins Univ. Press, Baltimore, 1996

Teaching methods -
Last update: doc. RNDr. Iveta Hnětynková, Ph.D. (06.10.2017)

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.

Requirements to the exam -
Last update: doc. RNDr. Iveta Hnětynková, Ph.D. (28.10.2019)

The final exam has written and oral part and covers all material presented in lectures and practicals during the semester. A student, who does not pass the written part is not allowed to continue to the oral part and fails the exam. A student, who does not pass the oral part also fails the exam. In both cases, it is necessary to repeat both parts of the exam.

Syllabus -
Last update: doc. RNDr. Iveta Hnětynková, Ph.D. (03.09.2020)

1. A brief overview of related topics from previous courses (the Schur decomposition, the QR decomposition, the LU decomposition, the singular value decomposition).

2. Solution of linear approximation problems (the least squares method, the total least squares method, generalizations).

3. Krylov subspaces (the Arnoldi and the Lanczos method for computation of a basis, connections to Jacobi matrices, applications).

4. Krylov subspace methods. Comparison of short a long recurrences (loss of orthogonality, stability, prize), Faber-Manteuffel theorem.

5. The conjugate gradient (CG) method, MINRES method.

6. The generalized minimal residual method (GMRES), FOM method. Overview of other Krylov subspace methods.

7. Matrix functions (definition, evaluation, apllications).

8. Special matrices (definition of selected matrices of special structure and properties, applications).

 
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