Matrix analysis and variational calculus

Type of study	Bachelor
Language of instruction	Czech
Code	310-3142/01
Abbreviation	MVA
Course title	Matrix analysis and variational calculus
Credits	2
Coordinating department	Department of Mathematics and Descriptive Geometry
Course coordinator	prof. RNDr. Radek Kučera, Ph.D.

Subject syllabus

Week. Lecture
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1st Vector space, linear mappings and matricies.
2nd Scalar product and orthogonality, orthogonalization procedure.
3rd Eigenvalues and eigenvectors, spectral decomposition.
4th Singular values and singular decomposition. Generalized inverse.
5th Matrix factorizations. Fast solving of linear systems.
6th Gradient descent method. Preconditioning.
7th Linear, bilinear and quadratic forms. Classification.
8th Weak solutions of differential equations.
9th Theorems on existence of weak solutions.
10th Variational solving differential equations. Ritz-Galerkin method.
11th Fundamentals of the finite element method.
12th Model boundary value problems for ODEs.
13th Model boundary value problems for PDEs.
14th Comparision with the finite difference method.

Literature

1. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999, .
2. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007, ISBN: 978-3-540-34658-6.
3. Golub G.H., Loan C.F.V.: Matrix Computation. The Johns Hopkins University Press, Baltimore, 1996, ISBN 0-8018-5414-8.

Advised literature

1. A. Tveito, R. Winther: Introduction to Partial Differential Equations: A Computational Approach. Springer, Berlin, 2000.
2. http://mi21.vsb.cz/

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