M7750 Matrix and Optimisation Numerical Methods

Faculty of Science
Autumn 2018
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 17. 9. to Fri 14. 12. Mon 16:00–17:50 M6,01011
  • Timetable of Seminar Groups:
M7750/01: Mon 17. 9. to Fri 14. 12. Tue 13:00–13:50 MP2,01014a, J. Zelinka
Prerequisites
Basic of calculus and linera algebra, basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This course complements the basic numerical methods, which are transmitted in courses Numerical methods I and II. Its aim is to acquaint students with the main optimization numerical methods and numerical methods of linear algebra. Emphasis is placed on methods that are used in other lectures, especially statistics. After completing the course, students should be able not only to efficiently use existing methods using existing software, but also create their own implementations of the algorithms.
Syllabus
  • Introduction (block operations with matrices   - inversion and determinant, permutation matrices, Kronecker product).
  • Least Squares Method (classic approach and the approach of using Moore-Penrose pseudoinverse.
  • Matrix decomposition and their use (LU decomposition, Cholesky decomposition, singular value decomposition, QR decomposition).
  • Other methods (calculating eigenvalues and vectors root of positive semi-definite matrix, etc.).
  • Optimization methods (golden ratio, Nelderova-Mead method).
Literature
    recommended literature
  • MATHEWS, John H. and Kurtis D. FINK. Numerical methods using MATLAB. 4th ed. Upper Saddle River, N.J.: Pearson, 2004, ix, 680. ISBN 0130652482. info
  • GOLUB, Gene H. and Charles F. VAN LOAN. Matrix computations. 3rd ed. Baltimore, Md.: Johns Hopkins University Press, 1996, xxvii, 694. ISBN 0801854148. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
Teaching methods
Lectures 2h.
Exercises 1h.
Assessment methods
Oral exam
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2016, autumn 2017.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2018/M7750