Course: Large Systems of Equations 2

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Course title Large Systems of Equations 2
Course code KMA/RVSR2
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • 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 Bunch-Parlett 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 conjugate-gradient-type 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.
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.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Mathematics (2014) Mathematics courses 1 Summer
Faculty of Science Computer Science (2015) Informatics courses - Summer
Faculty of Science Applied Computer Science (1) Informatics courses - Summer