M7PNM1 Advanced numerical methods I

Faculty of Science
Autumn 2026
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. Mgr. Jan Koláček, Ph.D. (lecturer)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. Mgr. Jan Koláček, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 12:00–13:50 M2,01021
  • Timetable of Seminar Groups:
M7PNM1/01: Thu 12:00–13:50 MP1,01014, J. Zelinka
M7PNM1/02: Thu 8:00–9:50 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
Abstract
This course follows up on the basic numerical methods, which are transmitted in courses Numerical methods I and II. Its aim is to acquaint students with the main numerical methods of linear algebra and with their application to both standard and special matrices. Emphasis is placed on methods that are used in other lectures. 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.
Learning outcomes
Student will be able to:
- to find and apply basic matrix decompositions
- to use a suitable numerical method to find the matrix's own numbers
- to apply selected algorithms for some special types of matrices
- to use an advanced iterative method to find the solution of the system of linear equation
Key topics
  • Introduction (repetition of some terms, block operations with matrices, permutation matrices, ...).
  • Least Squares Method (classic approach and the approach of using Moore-Penrose pseudoinverse), non-linear least squares.
  • Matrix decomposition and their use (LU decomposition, Cholesky decomposition, singular value decomposition, QR decomposition).
  • Advanced methods for solving a system of nonlinear equations.
  • Some special types of matrices.
  • Eigenvalues and eigenvectors.
  • Numerical stability of matrix calculations.
  • Other methods (root of positive semi-definite matrix, matrix functions etc.).
  • Sparse matrices
Study resources and literature
    recommended literature
  • GOLUB, Gene H. and Charles F. VAN LOAN. Matrix computations. ČTH. ed. Baltimore, Md.: Johns Hopkins University Press, 2013, 756 pp. ISBN 1-4214-0794-9. URL info
  • DATTA, Biswa Nath. Numerical linear algebra and applications. 2nd. SIAM, 2010, 554 pp. ISBN 0-89871-765-5. URL info
  • MATHEWS, John H. and Kurtis D. FINK. Numerical methods using MATLAB. 4th ed. Upper Saddle River: Pearson, 2004, ix, 680. ISBN 0130652482. info
  • Speciální matice a jejich použití v numerické matematice (Orig.) : Special matrices and their applications in numerical mathematics [Fiedler, 1984]. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
Approaches, practices, and methods used in teaching
Lectures 2h.
Exercises 2h.
Method of verifying learning outcomes and course completion requirements
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 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024, Autumn 2025.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2026/M7PNM1