457-0921/01 – Iterative Methods (IM)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantorprof. RNDr. Radim Blaheta, CSc.Subject version guarantorprof. RNDr. Radim Blaheta, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1995/1996Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
BLA19 prof. RNDr. Radim Blaheta, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 2+0

Subject aims expressed by acquired skills and competences

Student bude umět použít různé typy iteračních metod pro řešení úloh lineárních i nelineárních soustav. Bude znát základní myšlenky i některé nejnovější výsledky daného oboru.

Teaching methods

Summary

Předmět seznamuje s různými typy iteračních metod pro řešení úloh lineární algebry. Výklad je soustředěn na základní myšlenky, zahrnuje však i nejnovější výsledky daného oboru. Přednáška navazuje na předměty: "Matematické modelování a metoda konečných prvků" a "Maticová analýza".

Compulsory literature:

Stoer, R. Bulirsch: Introduction to numerical analysis, Springer, NY 1993. Axelsson: Iterative solution methods, Cambridge Univ. Press, 1994. Hackbusch: Iterative solution of large sparse systems of equations, Springer, NY 1994. Barrett et. al.: Templates for the solution of linear systems, SIAM, Philadelphia 1993. Smith, P.Bjorstadt, W.Gropp: Domain Decomposition, Camb-ridge Univ.Press, 1996.

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: Vlastnosti matic. Spektrální vlastnosti symetrických matic. Symetrie a pozitivní definitnost (SPD). Matice vznikající při diskretizaci okrajových úloh. Klasické iterační metody. Richardsonova, Jacobiho a Gaussova-Seidelova iterační metoda. Analýza konvergence pro SPD matice. Číslo podmíněnosti. Konvergence Gaussovy - Seidelovy metody. Předpodmínění. Metoda sdružených gradientů (MSG). Odvození metody. Konvergence a odhad chyby. Srovnání s klasickými iteračními metodami. MSG s předpodmíněním - algoritmus s explicitní a implicitní transformací soustavy. Předpodmínění neúplnou faktorizací. Konstrukce předpodmínění. Modifikovaná neúplná faktorizace. Diagonální kompenzace. Neúplná faktorizace pro matice vznikající z úloh pružnosti. Víceúrovňové (multigridní) iterační metody. Dvouúrovňová metoda pro modelovou úlohu. Hlazení. Korekce na hrubé síti. Analýza konvergence. Víceúrovňové metody. Techniky rozložení oblasti. Substruktury. Aditivní a multiplikativní Schwarzova metoda. Použití pro předpodmínění. Paralelizace. Technika kompozitních sítí. Efektivní a paralelní implementace iteračních metod.

Conditions for subject completion

Combined form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 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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