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master's thesis
Schurova dekompozicija i primjene
2023. urn:nbn:hr:126:653934
Poljarević, Petar
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Poljarević, P. (2023). Schurova dekompozicija i primjene (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:653934

Poljarević, Petar. "Schurova dekompozicija i primjene." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:653934

Poljarević, Petar. "Schurova dekompozicija i primjene." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:653934

Poljarević, P. (2023). 'Schurova dekompozicija i primjene', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 26 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:653934

Poljarević P. Schurova dekompozicija i primjene [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 December 26] Available at: https://urn.nsk.hr/urn:nbn:hr:126:653934

P. Poljarević, "Schurova dekompozicija i primjene", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:653934

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Metadata
TitleSchurova dekompozicija i primjene
Title (english)Schur Decomposition And Its Applications
AuthorPetar Poljarević
MentorZoran Tomljanović (mentor)
Committee memberKristian Sabo (predsjednik povjerenstva)
Committee memberZoran Tomljanović (član povjerenstva)
Committee memberIvana Kuzmanović Ivičić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Numerical Mathematics
Abstract
U ovome radu bavit ćemo se Schurovom dekompozicijom kvadratnih matrica te njenim najvažnijim praktičnim primjenama. U prvom dijelu rada navest ćemo neke osnovne pojmove i tvrdnje iz područja linearne algebre koje će nam biti važne za razumijevanje ostatka rada. U drugom dijelu pokazat ćemo egzistenciju Schurove dekompozicije za proizvoljnu kvadratnu matricu, kao i egzistenciju realne Schurove dekompozicije za proizvoljnu realnu kvadratnu matricu. Nakon toga, izgradit ćemo numerički stabilan i učinkovit algoritam za računanje Schurove dekompozicije pod nazivom QR algoritam te ćemo navesti nekoliko ideja za njegovo ubrzanje. U trećem i posljednjem dijelu rada pokazat ćemo neke fundamentalne primjene Schurove dekompozicije, kao što su računanje svojstvenih vrijednosti zadane matrice, računanje nultočaka polinoma proizvoljnog stupnja, računanje matrične eksponencijalne funkcije te rješavanje Ljapunovljevih i Sylvesterovih matričnih jednadžbi.
Abstract (english)
In this paper, we will observe Schur decomposition of square matrices, as well as its most important practical applications. In the first chapter of this paper, we will list some basic terms and statements from the field of linear algebra that will be important during the remaining chapters. In the second chapter, we will show the existence of Schur decomposition for any given square matrix, as well as the existence of real Schur decomposition for any given real square matrix. After that, we will introduce a numerically stable and efficient algorithm used for computing the Schur decomposition called The QR algorithm and we will also list a few ideas we can use to make the algorithm run faster. In the third and the final chapter of this paper, we will show some fundamental applications of Schur decomposition, such as computing the eigenvalues of a given matrix, computing the roots of a polynomial of any degree, computing the matrix exponential function, and solving Lyapunov and Sylvester matrix equations.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:653934
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-11-06 11:18:51