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 2norm 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 2norm 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/studentpapers/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
 LUNFNA40152017
 ISSN
 16546229
 other publication id
 2017:K12
 language
 English
 id
 8921456
 date added to LUP
 20191126 13:13:29
 date last changed
 20191126 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 2norm 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 = {16546229}, 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}, }