prikaz prve stranice dokumenta SVD dekompozicija i primjene
  Download
PDF 1.62 MB
undergraduate thesis
SVD dekompozicija i primjene
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. urn:nbn:hr:126:714160
Hrnjkaš, Mihaela
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Numerical Mathematics Research Group

Cite this document

Hrnjkaš, M. (2018). SVD dekompozicija i primjene (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:714160

Hrnjkaš, Mihaela. "SVD dekompozicija i primjene." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:714160

Hrnjkaš, Mihaela. "SVD dekompozicija i primjene." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:714160

Hrnjkaš, M. (2018). 'SVD dekompozicija i primjene', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 02 April 2023, https://urn.nsk.hr/urn:nbn:hr:126:714160

Hrnjkaš M. SVD dekompozicija i primjene [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2023 April 02] Available at: https://urn.nsk.hr/urn:nbn:hr:126:714160

M. Hrnjkaš, "SVD dekompozicija i primjene", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:714160

Please login to the repository to save this object to your list.
Metadata
TitleSVD dekompozicija i primjene
Title (english)SVD Decomposition and Applications
AuthorMihaela Hrnjkaš
MentorZoran Tomljanović (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics)
(Numerical Mathematics Research Group)
Osijek
Defense date and country2018-09-19, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Numerical Mathematics
Abstract
U prvome dijelu ovoga rada definirat ćemo pojam dekompozicije na singularne vrijednosti te iskazati i dokazati teorem koji govori o egzistenciji ove dekompozicije. Spomenut ćemo neka od najvažnijih svojstava te uočiti poveznicu između singularnih i svojstvenih vrijednosti. U drugome dijelu rada dotaknut ćemo se primjena dekompozicije na singularne vrijednosti. Ukratko ćemo se upoznati s linearnim problemom najmanjih kvadrata te opisati primjenu SVD dekompozicije. Spomenut ćemo kompresiju slike te na primjeru ilustrirati primjenu dekompozicije na singularne vrijednosti u kompresiji koristeći se svojstvom aproksimacije matricom nižeg ranga.
Abstract (english)
In the first part of this paper, we will define the concept of singular value decomposition and prove the theorem that states the existence of singular value decomposition. Some of the most important properties will also be mentioned and connection between eigenvalues and singular values will be noticed. In the second part of the paper, attention will be given to applications of singular value decomposition. A brief introduction to linear least square problem will be followed by application of singular value decomposition to this problem. Also, we will touch upon an image compression and illustrate the usage of SVD decomposition in compression using the property of a low-rank matrix approximation.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:714160
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
Terms of useLicence In copyright icon
RepositoryRepository of Department of Mathematics Osijek
Created on2018-10-18 06:11:02