470-2203/01 – Linear Algebra with Matlab (LAM)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantordoc. Ing. Dalibor Lukáš, Ph.D.Subject version guarantordoc. Ing. Dalibor Lukáš, Ph.D.
Study levelundergraduate or graduateRequirementOptional
YearSemesterwinter
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
MER126 Ing. Michal Merta, Ph.D.
POS220 Ing. Lukáš Pospíšil, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

To expand the knowledge of the students using Matlab by concepts that are important in understanding of modern methods used in informatics and numerical solution of engineering problems.

Teaching methods

Lectures
Tutorials
Project work

Summary

Advanced concepts of linear algenra are key ingredients in solving of many engineering problems such as signal analysis, implemetation of search engins, optimal control or numerical solution of differential equations. In this course, the students can expand their knowledge of linear algebra using Matlab by working knowledge of concepts that are important in understanding of modern methods used in informatics and numerical solution of engineering problems with a special stress on matrix decompositions and the spectral theory.

Compulsory literature:

G. Strang, Linear Algebra and its Application, Academic Press, New York 1980. G. H. Golub, and C. van Loan, Matrix Computations, The John Hopkins University Press, London 1989. L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM Philadelphia 1997. ISBN 0-89871-361-7.

Recommended literature:

L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM Philadelphia 1997. ISBN 0-89871-361-7.

Way of continuous check of knowledge in the course of semester

Conditions for credit: Project (minimum 15 points).

E-learning

Další požadavky na studenta

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Introduction to MATLAB (overview of toolboxes and functions, help, basic elements, editing of the n-dimensional arrays). MATLAB programming (control flow statements, 2D and 3D graphics). Advanced MATLAB functions (graphical user interface). Analytic geometry (computation of the inclinations and distances in 2D and 3D). Sparse matrix structures (band, profile, row compressed, column compressed). Solution of the linear algebraic systems (nonsingular, underdetermined and overdetermined systems). Gauss elimination (row and column versions, pivotization). LU and Choleski decomposition (row and column versions, pivotization). Reordering algorithms (SYMAMD, COLAMD, SLOAN, RCM). QR decomposition (Givens and Householder transforms). Eigenvalues and spectral decomposition (QR and LR algorithms, shift). Singular decomposition, pseudoinverse. Lanczos method and conjugate gradient method. Project presentation. Exercises: Introduction to MATLAB, functions overview, editing of the n-dimensional arrays. MATLAB programming techniques, the use of the control flow statements, 2D and 3D graphic functions). Graphical user interface implementation. Computation of the inclinations and distances in 2D and 3D). Sparse matrix structures implementation (band, profile, row compressed, column compressed). Solvers of the linear algebraic systems (nonsingular, underdetermined and overdetermined systems). Solution of the linear algebraic system using Gauss elimination (row and column versions, pivotization). Solution of the linear algebraic system using LU and Choleski decomposition (row and column versions, pivotization). Application of the reordering algorithms (SYMAMD, COLAMD, SLOAN, RCM). The use of the QR decomposition (implementation, Givens and Householder transforms, applications). Computation of the eigenvalues and spectral decomposition (implementation, QR and LR algorithms, shift, applications). Computation of the singular decomposition and pseudoinverse (implementation, application). Lanczos method and conjugate gradient method (implementation, applications). Project presentation. Projects: Application oriented project in MATLAB (max. 30 points).

Conditions for subject completion

Full-time form (validity from: 2010/2011 Winter semester, validity until: 2010/2011 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100  51
        Exercises evaluation Credit  
        Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
V - ECTS - bc. 2011/2012 Full-time Czech Optional 401 - Study Office stu. block