### Course: Numerical Methods of Algebra

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 Course title Numerical Methods of Algebra KMD/NMA Lecture + Lesson Bachelor not specified Winter and summer 5 Czech Optional Face-to-face Course does not contain work placement None
Lecturer(s)
• Plešinger Martin, doc. Ing. Ph.D.
Course content
Lecture: 01. Applied and numerical mathematics, origin of errors in computations. 02. Floating point arithmetic, rounding errors. Problem sensitivity and backward stability. 03. Eigenvalue and its sensitivity. 04. Solution of linear algebraic systems and its sensitivity. 05. Error estimation and bacward stability. 06. Orthogonal transformations and the QR decomposition. 07. Gauss elimination and the LU decomposition. 08. Singular value decomposition and its applictaions. 09. The least squares and total least squares problems. 10. Computing of all eigenvalues, QR algorithm. 11. Computing of some eigenvalues, power mehod. Lanczos and Arnoldi methods. 12. Iterative methods for solving linear systems. 13. The conjugate gradient method. 14. The MinRES and GMRES method. Practise: 01. Practise: Applied and numerical mathematics, origin of errors in computations. 02. Practise: Floating point arithmetic, rounding errors. Problem sensitivity and backward stability. 03. Practise: Eigenvalue and its sensitivity. 04. Practise: Solution of linear algebraic systems and its sensitivity. 05. Practise: Error estimation and bacward stability. 06. Practise: Orthogonal transformations and the QR decomposition. 07. Practise: Gauss elimination and the LU decomposition. 08. Practise: Singular value decomposition and its applictaions. 09. Practise: The least squares and total least squares problems. 10. Practise: Computing of all eigenvalues, QR algorithm. 11. Practise: Computing of some eigenvalues, power mehod. Lanczos and Arnoldi methods. 12. Practise: Iterative methods for solving linear systems. 13. Practise: The conjugate gradient method. 14. Practise: The MinRES and GMRES method.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
• Class attendance - 56 hours per semester
Learning outcomes
The course is focused on extending the knowledge of numerical methods, their computer implementations and practical usage. Understanding the principles of the methods and their limitations is the main goal.
Students will acquire basic knowledge of scientific computing and numerical linear algebra methods, especially the methods for solving systems of linear equations.
Prerequisites
Basic linear algebra course.

Assessment methods and criteria
Combined examination

Requirements for getting a credit are activity at the practicals /seminars and successful passing the tests. Examination is of the written and oral forms.
Recommended literature
• A. Greenbaum. Iterative Methods for Solving Linear Systems. SIAM, 1997.
• Demmel, J.W. Applied Numerical Linear Algebra. SIAM, 1997.
• Duintjer-Tebbens, E. J. a kol. Analýza metod pro maticové výpočty, základní metody. Matfyzpress. 2012.
• Fiedler, M.:. Speciální matice a jejich použití v numerické matematice.. SNTL Praha, 1981.
• Trefethen, L.N., Bau, D. Numerical Linear Algebra. SIAM, 1997.
• Watkins D.S. Fundamentals of Matrix Computations.. Jon Wiley & Sons, NY, USA, 1991. ISBN 0-471-61414-9.

 Study plans that include the course
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Faculty: Faculty of Science, Humanities and Education Study plan (Version): Professional studies for lower-secondary school teachers. (15) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: -
Faculty: Faculty of Science, Humanities and Education Study plan (Version): Education in Leisure Time (20) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: -
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