Lecturer(s)


Netuka Horymír, RNDr. Ph.D.

Course content

1. Elimination trees and their meaning. 2. Symbolic factorization using elimination trees. 3. Large sparse indefinite systems. 4. The BunchParlett method: types of pivots, phases of solution process, stability conditions, minimum degree algorithm for indefinite systems, the Markowitz strategy of pivot choice. 5. The conjugate gradient method with preconditioning. 6. Computer realization, termination criteria. 7. Solution of indefinite and unsymmetric systems using conjugategradienttype methods. 8. Introduction to multigrid methods.

Learning activities and teaching methods

Lecture, Monologic Lecture(Interpretation, Training)
 Attendace
 39 hours per semester
 Semestral Work
 20 hours per semester
 Preparation for the Exam
 30 hours per semester

Learning outcomes

Understand computational methods for solving of large sparse positive definite systems of equations.
Knowledge Gain knowledge of computational technologies useful for solution of large sparse systems of equations.

Prerequisites

Standard knowledge from linear algebra. Information concerning numerical methods and graph theory are welcomed, but not necessary. Elemental experience with computation on PC and programming ability (not on the professional level). Student has to pass the first part of the course (KMA/RVSR1).

Assessment methods and criteria

Oral exam, Seminar Work
Credit: the student has to compute assigned examples or to do a seminar work. Exam: the student has to understand the subject and be acquainted with theory and particular algorithms.

Recommended literature


I. S. Duff, A. M. Erisman, J. K. Reid. (1997). Direct Methods for Sparse Matrices. Claredon Press, Oxford.

O. Axelsson, V. A. Barker. (1984). Finite Element Solution of Boundary Value ProblemsTheory and Computation. Academic Press.

T. A. Davis. (2006). Direct methods for sparse linear systems. SIAM, Philadelphia.
