457-0002/01 – Numerical Analysis I. (NUM1)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. Mgr. Vít Vondrák, Ph.D.Subject version guarantordoc. Mgr. Vít Vondrák, Ph.D.
Study levelundergraduate or graduateRequirementChoice-compulsory
YearSemestersummer
Study languageCzech
Year of introduction1992/1993Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesMaster
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

Teaching methods

Summary

Errors in numerical computations. Solution of nonlinear equations: fixed point theorem, Newton's method. Iterative solution of system of linear equations. Finding eigenvalues and eigenvectors of matrices. Polynomial, trigonometric and spline interpolation. Approximation: least square method, Tchebyshevian approximation. Numerical differentiation and integration. Numerical solution of ordinary differential equations with initial condition.

Compulsory literature:

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: 1. Úvod do numerických metod Zobrazení čísel na počítači, typy chyb a jejich analýza. 2. Řešení nelineárních rovnic Věta o pevném bodě, metoda prostých iterací, Newtonova metoda, řešení soustav nelineárních rovnic. 3. Iterační metody řešení soustav lineárních rovnic Jacobiova metoda, metoda sdružených gradientů, předpodmínění. 4. Vlastní čísla a vektory matic I Částečný problém vlastních čísel: mocninná metoda, redukční metody. 5. Vlastní čísla a vektory matic II Úplný problém vlastních čísel: Givensova, Householderova. 6. Interpolace Lagrangeův a Newtonův interpolační polynom, trigonometrická interpolace, interpolace pomocí spline funkcí. 7. Aproximace Metoda nejmenších čtverců, Čebyševova aproximace. 8. Numerická derivace 9. Numerická integrace Newtonovy-Cotesovy vzorce, Gaussova kvadratura, Richardsonova extrapolace. 10. Numerické řešení počátečních úloh pro obyčejné diferenciální rovnice I Jednokrokové metody. 11. Numerické řešení počátečních úloh pro obyčejné diferenciální rovnice II Vícekrokové metody.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2007/2008 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
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2007/2008 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2301) Mechanical Engineering (2301T777) Mechanical Engineering / not obligatory subject P Czech Ostrava 5 Optional study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 3 Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2301) Mechanical Engineering (2301T777) Mechanical Engineering / not obligatory subject P Czech Ostrava 5 Optional study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 3 Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (B2612) Electrical Engineering and Computer Science (1801R001) Computer Science P Czech Ostrava 3 Choice-compulsory study plan
2002/2003 (M2301) Mechanical Engineering (2301T777) Mechanical Engineering / not obligatory subject P Czech Ostrava 5 Optional study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 3 Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2301) Mechanical Engineering (2301T777) Mechanical Engineering / not obligatory subject P Czech Ostrava 5 Optional study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 3 Choice-compulsory study plan
2000/2001 (M2301) Mechanical Engineering (2301T777) Mechanical Engineering / not obligatory subject P Czech Ostrava 5 Optional study plan
2000/2001 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 3 Choice-compulsory study plan

Occurrence in special blocks

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