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Course, academic year 2023/2024
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Numerical Linear Algebra - NNUM006
Title: Numerická lineární algebra
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 6
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: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. Ing. Zdeněk Strakoš, DrSc.
Classification: Mathematics > Numerical Analysis
Incompatibility : NMNM331
Interchangeability : NMNM331
Is incompatible with: NMNM931, NMNM331, NNUM032, NNUM031
Is pre-requisite for: NNUM007
Is interchangeable with: NMNM931, NMNM331
In complex pre-requisite: NMNM332
Annotation -
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 builds upon the knowlegde of basic numerical methods (the course NNUM105), and emphasizes formulation of questions, motivation and interconnections.
Last update: T_KNM (22.05.2008)
Aim of the course -

The course gives students a knowledge of fundamentals of numerical linear algebra with the concetration on methods for solving linear algebraic equations and on eigenvalue problems.

Last update: T_KNM (17.05.2008)
Literature - Czech

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

Last update: T_KNM (17.05.2008)
Teaching methods -

Lectures and tutorials in a lecture hall.

Last update: T_KNM (17.05.2008)
Requirements to the exam -

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

Last update: STRAKOS/MFF.CUNI.CZ (29.04.2008)
Syllabus -

1. The Schur theorem, its consequences and connections.

2. Orthogonal transformations and QR decompositions.

3. The LU decomposition and its numerical stability.

4. The singular value decomposition, its theoretical and computational connections.

5. Least squares problems.

6. Partial eigenvalue problems. The Arnoldi method, the Lanczos method.

7. Iterative solution of linear algebraic systems. The conjugate gradient method and its generalizations. The generalized minimal residual method.

8. Computing of complete set of eigenvalues. The QR algoritm.

Last update: STRAKOS/MFF.CUNI.CZ (29.04.2008)
Entry requirements -

Students are expected to have attended the course NNUM105.

Last update: T_KNM (22.05.2008)
 
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