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undergraduate thesis
Primjena Cholesky dekompozicije na rješavanje linearnih sustava
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. urn:nbn:hr:126:316811
Mikić, Magdalena
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Institutional repository: Repository of School of Applied Mathematics and Computer Science

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Mikić, M. (2022). Primjena Cholesky dekompozicije na rješavanje linearnih sustava (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:316811

Mikić, Magdalena. "Primjena Cholesky dekompozicije na rješavanje linearnih sustava." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:316811

Mikić, Magdalena. "Primjena Cholesky dekompozicije na rješavanje linearnih sustava." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:316811

Mikić, M. (2022). 'Primjena Cholesky dekompozicije na rješavanje linearnih sustava', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 30 June 2024, https://urn.nsk.hr/urn:nbn:hr:126:316811

Mikić M. Primjena Cholesky dekompozicije na rješavanje linearnih sustava [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2024 June 30] Available at: https://urn.nsk.hr/urn:nbn:hr:126:316811

M. Mikić, "Primjena Cholesky dekompozicije na rješavanje linearnih sustava", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:316811

Metadata
TitlePrimjena Cholesky dekompozicije na rješavanje linearnih sustava
Title (english)Application of Cholesky Decomposition to Solving Linear Systems
AuthorMagdalena Mikić
MentorSuzana Miodragović (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-09-19, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Numerical Mathematics
Abstract
U ovom ćemo radu izvesti Cholesky dekompoziciju matrice i pokazati kako se ona primjenjuje na rješavanje nekih specifičnih sustava linearnih jednadžbi. Najprije ćemo navesti osnovne pojmove i rezultate vezane uz linearne sustave te metode rješavanja linearnih sustava. Nakon toga, definirat ćemo simetrične matrice i iskazati važne tvrdnje vezane uz pozitivnu definitnost simetričnih matrica. Pokazat ćemo jedinstvenost Cholesky dekompozicije, kao i ekvivalenciju između pozitivne definitnosti simetrične matrice te postojanja i jedinstvenosti dekompozicije. Navest ćemo algoritam kojim dolazimo do dekompozicije i na primjeru pokazati kako matricu rastaviti koristeći navedeni algoritam. Objasnit ćemo postupak rješavanja linearnog sustava koristeći Cholesky dekompoziciju, takozvanu Cholesky metodu, i ilustrirati ga primjerom. Na kraju ćemo ukratko objasniti \(LDL^{T}\) dekompoziciju, kao posebnu varijantu Cholesky dekompozicije.
Abstract (english)
In this paper, we will derive the Cholesky decomposition of matrix and show how it can be used for solving some specific systems of linear equations. Firstly, we will state basic terms and results related to linear systems and methods of solving them. After that, we will define symmetric matrices and state the important statements regarding the positive definiteness of symmetric matrices. We will prove the uniqueness of the Cholesky decomposition and the equivalence between positive definiteness of symmetric matrices and existence and uniqueness of decomposition. We will state the algorithm by which we get the decomposition and show an example of how to decompose the matrix using the specified algorithm. We will explain the procedure for solving a linear system using the Cholesky decomposition, the so-called Cholesky method, and illustrate it with an example. Finally, we will briefly explain the \(LDL^{T}\) decomposition, as a special variant of the Cholesky decomposition.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:316811
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
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Created on2022-09-21 06:35:44