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The Golub-Kahan method of computing a Singular Value Decomposition

Bogers, Evelien LU (2023) In Bachelor's Theses in Mathematical Sciences NUMK11 20222
Centre for Mathematical Sciences
Mathematics (Faculty of Sciences)
Abstract
This BSc thesis looks into the Golub-Kahan method for computing Singular Value
Decompositions (SVD). Computing an SVD is expensive but can be worth it in some
cases. This decomposition shows any near rank deficiency that might cause problems
when solving Least Squares problems. The Golub-Kahan algorithm exploits the
implicit symmetric QR algorithm to efficiently compute an SVD. A matrix is first
bidiagonalized by Householder reflections, after which the Golub-Kahan SVD step is
applied. This step implicitly applies the symmetric QR algorithm to the previously
bidiagonalized matrix. The Golub-Kahan algorithm is more efficient and preferable
to the Jacobi method for reducing a symmetric matrix to diagonal form. In this
thesis, we... (More)
This BSc thesis looks into the Golub-Kahan method for computing Singular Value
Decompositions (SVD). Computing an SVD is expensive but can be worth it in some
cases. This decomposition shows any near rank deficiency that might cause problems
when solving Least Squares problems. The Golub-Kahan algorithm exploits the
implicit symmetric QR algorithm to efficiently compute an SVD. A matrix is first
bidiagonalized by Householder reflections, after which the Golub-Kahan SVD step is
applied. This step implicitly applies the symmetric QR algorithm to the previously
bidiagonalized matrix. The Golub-Kahan algorithm is more efficient and preferable
to the Jacobi method for reducing a symmetric matrix to diagonal form. In this
thesis, we present a theoretical analysis and a programming part regarding this
process. (Less)
Popular Abstract (Swedish)
Vi är omgivna av stora mängder data. Data kan lagras i stora datablock, så kallade matriser. Om mängden data är väldigt stor, blir dessa datablock svårahanterliga. Singulärvärdesfaktorisering är en metod som tillämpas på matriser för att göra datan de representerar mer lätthanterlig. Den här uppsatsen diskuterar metoden.
Please use this url to cite or link to this publication:
author
Bogers, Evelien LU
supervisor
organization
course
NUMK11 20222
year
type
M2 - Bachelor Degree
subject
keywords
singular value decomposition, singular value, numerical analysis, golub-kahan, householder, givens, mathematics
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUNFNA-4043-2023
ISSN
1654-6229
other publication id
2023:K5
language
English
id
9112096
date added to LUP
2025-06-25 15:42:17
date last changed
2025-06-25 15:42:17
@misc{9112096,
  abstract     = {{This BSc thesis looks into the Golub-Kahan method for computing Singular Value
Decompositions (SVD). Computing an SVD is expensive but can be worth it in some
cases. This decomposition shows any near rank deficiency that might cause problems
when solving Least Squares problems. The Golub-Kahan algorithm exploits the
implicit symmetric QR algorithm to efficiently compute an SVD. A matrix is first
bidiagonalized by Householder reflections, after which the Golub-Kahan SVD step is
applied. This step implicitly applies the symmetric QR algorithm to the previously
bidiagonalized matrix. The Golub-Kahan algorithm is more efficient and preferable
to the Jacobi method for reducing a symmetric matrix to diagonal form. In this
thesis, we present a theoretical analysis and a programming part regarding this
process.}},
  author       = {{Bogers, Evelien}},
  issn         = {{1654-6229}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor's Theses in Mathematical Sciences}},
  title        = {{The Golub-Kahan method of computing a Singular Value Decomposition}},
  year         = {{2023}},
}