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Topics on Numerical and Applied Linear Algebra 1 - NNUM130

Title:	Témata z numerické a aplikované lineární algebry 1
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, 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
Is incompatible with:	NMNV407

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Annotation -

Last update: T_KNM (18.05.2008)

This course should extend and strenghten theoretical foundations of methods of numerical linear algebra. Its main goals are: to present an introduction into perturbation theory and numerical stability; 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. Prerequisites: NNUM006, NNUM042.

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] N.J. Higham, Accuracy and stability of numerical algorithms (second edition), SIAM, Philadelphia, PA, 2002

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

[4] G. Meurant and Z. Strakoš, The Lanczos and conjugate gradient algorithms in finite precision arithmetic, Acta Numerica, 15, pp. 471-542, 2006

[5] S.G. Nash (Ed.), A history of scientific computing (Papers from the Conference on the History of Scientific and Numeric Computation held at Princeton University, Princeton, ACM Press, New York, 1990

[6] B.N. Parlett, The symmetric eigenvalue problem, SIAM, Philadelphia, 1998

[7] D.P. O'Leary, Z. Strakoš and P. Tichý, On sensitivity of Gauss-Christoffel quadrature, Numerische Mathematik, accepted for publication, 2007

[8] I. Hnětynková and Z. Strakoš, Lanczos tridiagonalization and core problems, Linear Algebra and its Applications, 421, pp. 243-251, 2007

[9] Z. Strakoš, D.P. O'Leary, C.C. Paige and P. Tichý, On unexpected consequences of numerical stability analysis of Krylov subspace methods, zvaná plenární přednáška, 22nd Biennial Conference on NA, Dundee, June 2007

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

[11] 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: STRAKOS/MFF.CUNI.CZ (30.04.2008)

Oral exam reflecting the content of the course.

Syllabus -

Last update: T_KNM (18.05.2008)

1. Introduction to perturbation theory and to numerical stability.

2. The Lanczos tridiagonalization, the method of conjugate gradients and Gauss-Christoffel quadrature, their relationship.

3. Gauss quadrature from the view of analysis, algebra and numerical metods.

4. Golub-Kahan bidiagonalization and core problem in linear algebraic models.

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.