Strategies for computing the condition number of a matrix
(2017) In Bachelor's Theses in Mathematical Sciences NUMK01 20171Mathematics (Faculty of Engineering)
- Abstract
- The main objective of this thesis is to present the article "An estimate of the condition number of a matrix", written by Cline et.al., which describes an algorithm for obtaining a reliable order of magnitude estimate of the condition number of a matrix in O(n^2) operations. In addition, the thesis introduces an iterative process for estimating the condition number in the 2-norm with arbitrary precision. It is a generalisation of the algorithm in the article, and it establishes a connection between power iteration and the algorithm from the article, and provides an alternative route to deriving its key equations. Also, the thesis covers basic theory surrounding the condition number, and for completeness it includes a brief presentation on... (More)
- The main objective of this thesis is to present the article "An estimate of the condition number of a matrix", written by Cline et.al., which describes an algorithm for obtaining a reliable order of magnitude estimate of the condition number of a matrix in O(n^2) operations. In addition, the thesis introduces an iterative process for estimating the condition number in the 2-norm with arbitrary precision. It is a generalisation of the algorithm in the article, and it establishes a connection between power iteration and the algorithm from the article, and provides an alternative route to deriving its key equations. Also, the thesis covers basic theory surrounding the condition number, and for completeness it includes a brief presentation on Skeel’s condition number which is based on the article Scaling for numerical stability in Gaussian elimination, written by Skeel
et.al.. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/8921456
- author
- Benzler Waaler, Per Niklas LU
- supervisor
-
- Claus Führer LU
- organization
- course
- NUMK01 20171
- year
- 2017
- type
- M2 - Bachelor Degree
- subject
- keywords
- condition, number, matrix, algorithm, skeel, Cline, svd
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFNA-4015-2017
- ISSN
- 1654-6229
- other publication id
- 2017:K12
- language
- English
- id
- 8921456
- date added to LUP
- 2019-11-26 13:13:29
- date last changed
- 2019-11-26 13:13:29
@misc{8921456, abstract = {{The main objective of this thesis is to present the article "An estimate of the condition number of a matrix", written by Cline et.al., which describes an algorithm for obtaining a reliable order of magnitude estimate of the condition number of a matrix in O(n^2) operations. In addition, the thesis introduces an iterative process for estimating the condition number in the 2-norm with arbitrary precision. It is a generalisation of the algorithm in the article, and it establishes a connection between power iteration and the algorithm from the article, and provides an alternative route to deriving its key equations. Also, the thesis covers basic theory surrounding the condition number, and for completeness it includes a brief presentation on Skeel’s condition number which is based on the article Scaling for numerical stability in Gaussian elimination, written by Skeel et.al..}}, author = {{Benzler Waaler, Per Niklas}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{Strategies for computing the condition number of a matrix}}, year = {{2017}}, }