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Strategies for computing the condition number of a matrix

Benzler Waaler, Per Niklas LU (2017) In Bachelor's Theses in Mathematical Sciences NUMK01 20171
Mathematics (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:
author
Benzler Waaler, Per Niklas LU
supervisor
organization
course
NUMK01 20171
year
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},
  keyword      = {condition,number,matrix,algorithm,skeel,Cline,svd},
  language     = {eng},
  note         = {Student Paper},
  series       = {Bachelor's Theses in Mathematical Sciences},
  title        = {Strategies for computing the condition number of a matrix},
  year         = {2017},
}