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Topics on Numerical and Applied Linear Algebra 2 - NNUM230

Title:	Témata z numerické a aplikované lineární algebry 2
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2012 to 2017
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. Ing. Zdeněk Strakoš, DrSc.
Classification:	Mathematics > Numerical Analysis

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KNM (18.05.2008)

This course should extend and strenghten theoretical foundations of methods of numerical linear algebra. It follows in the steps of the course NNUM130 with the goals: to extend knowledge about several modern methods; to emphasize analysis of the methods and algorithms, including effects of rounding errors; to use the studied topics for demonstration of connections between various mathematical tools and disciplines.

Aim of the course -

Last update: T_KNM (18.05.2008)

Theoretical foundations of methods of numerical linear algebra.

Literature - Czech

Last update: T_KNM (18.05.2008)

[1] G.H. Golub and C.F. Van Loan, Matrix computations (Third edition), Johns Hopkins University Press, Baltimore, MD, 1996

[2] A. Greenbaum, Iterative methods for solving linear systems, SIAM, Philadelphia, PA, 1997

[3] P.C. Hansen, Rank-deficient and discrete ill-posed problems: Numerical aspects of linear inversion, SIAM, Philadelphia, PA, 1998

[4] M. Arioli, V. Pták and Z. Strakoš, Krylov sequences of maximal length and convergence of GMRES, BIT Numerical Mathematics, 38, pp. 636-643, 1998

[5] C.C. Paige and Z. Strakoš, Core problems in linear algebraic systems, SIAM J. Matrix Analysis Appl., 27, 2006, pp. 861-875

[6] J. Liesen and Z. Strakoš, On optimal short recurrences for generating orthogonal Krylov subspace bases, SIAM Review, to appear

[7] J. Liesen and Z. Strakoš, On numerical stability in large scale numerical computations, ZAMM, 85, 2005, pp. 307-325,

[8] Z. Strakoš, Nonlinear problems in analysis of Krylov subspace methods, zvaná plenární přednáška, CFG07, Heidelberg, September 2007, www.cs.cas.cz/~strakos

[9] Z. Strakoš, Core problem theory in linear approximation problems, zvaná plenární přednáška, IMA Conference on Numerical Linear Algebra and Optimization, Birmingham, September 2007, www.cs.cas.cz/~strakos

[10] A. Antoulas, Approximation of large dynamical systems. SIAM, Philadelphia, 2005.

[11] C. Brezinski and L. Wuytack (Eds.): Numerical Analysis: Historical Developments in the 20th Century. Elsevier, Amsterdam, 2001.

[12] L. Eldén, Matrix methods in Data Mining and Pattern Recognition, SIAM, Philadelphia, 2007.

Teaching methods -

Last update: T_KNM (18.05.2008)

Lectures and discussions in a lecture hall.

Requirements to the exam -

Last update: T_KNM (18.05.2008)

Oral exam reflecting the content of the course.

Syllabus -

Last update: T_KNM (18.05.2008)

1. A general projection process and the problem of moments.

2. Krylov subspace methods as matching moments model reduction. Basic theory, stopping criteria, analysis of convergence, implementations, numerical stability, open problems.

3. Generalizations of the least squares problem; links between related methods in computational statistics and numerical linear algebra.

4. Hard numerical problems.

5. Nonlinear phenomena in numerical linear algebra.

Entry requirements -

Last update: T_KNM (18.05.2008)

The course assumes standard knowledge of linear algebra, calculus, elements of complex analysis, basic knowledge of numerical methods, including methods of numerical linear algebra. It is offered for students of various specializations starting from the seventh semester. Students are expected to have attended the courses NNUM006 and NNUM042.