470-2210/01 – Numerical Linear Algebra 1 (NLA1)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantordoc. Ing. Dalibor Lukáš, Ph.D.Subject version guarantordoc. Ing. Dalibor Lukáš, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KAB002 Ing. Pavla Hrušková, Ph.D.
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
MER126 Ing. Michal Merta, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 12+12

Subject aims expressed by acquired skills and competences

Linear algebra stands behind computer solutions to complex engineering problems. The course Numerical Linear Algebra 1 aims at helping students to classify problems of linear algebra and choose a proper algorithm for the solution regarding stability (sensitivity of the output data on the inputs) and computational complexity.

Teaching methods

Lectures
Tutorials
Project work

Summary

Linear algebra is a fundamental tool when formulating engineering problems and their efficient solution. This course is devoted to the related numerical methods and their efficient implementation.

Compulsory literature:

- J.D. Tebbens, I. Hnětynková, M. Plešinger, Z. Strakoš, P. Tichý - Analysis of Methods for Matrix Computations. Basic Methods. Matfyzpress Prague, 2012.

Recommended literature:

- G.H. Golab, C.F. Van Loan - Matrix Computations, 4th edition. The John Hopkins University Press, 2013.

Way of continuous check of knowledge in the course of semester

Test 10 pts.) Project (20 pts.)

E-learning

Other requirements

Successful defense of a semestral project. Students are familiar with fundamentals of linear algebra.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Systems of linear equations (nonsingular, underdetermined, and overdetermined). 2. Gaussian elimination method. 3. LU and Cholesky factorizations. 4. Sparse matrices. 5. QR factorization (Givens and Householder transform). 6. Eigenvalues and spectral decomposition (QR and LR algorithm, shift). 7. Cauchy contour integral method. 8. Singular value decomposition, matrix pseudoiverse. 9. Linear iterative solution methods (Jacobi, Gauss-Seidel, Richardson), convergence rates. 10. Chebyshev semi-iterative method, convergence rate. 11. Krylov space, method of conjugate gradients. 12. Rate of convergence of the conjugate gradient method, preconditioning. 13. Tři-diagonalization, Lanczos method. 14. Presentation of students projects.

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30 (30) 15
                Písemný test Written test 10  0
                Semestrální projekt Project 20  0
        Examination Examination 70 (70) 21
                Písemná část Written examination 55  0
                Ústní část Oral examination 15  0
Mandatory attendence parzicipation: bude doplněno

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (B0541A170008) Computational and Applied Mathematics VMI P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0541A170008) Computational and Applied Mathematics VMI K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0541A170008) Computational and Applied Mathematics VMI P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0541A170008) Computational and Applied Mathematics VMI K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner