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Using the QR Factorization to swiftly update least squares problems

Olsson, Oscar LU and Ivarsson, Tommy LU (2014) In Master’s Theses in Mathematical Sciences FMN820 20141
Mathematics (Faculty of Engineering)
Abstract
In this paper we study how to update the solution of the linear
system Ax = b after the matrix A is changed by addition or deletion
of rows or columns.
Studying the QR Factorization of the system, more specifically, the
factorization created by the Householder reflection algorithm, we find
that we can split the algorithm in two parts. The result from the first
part is trivial to update and is the only dependency for calculating
the second part.
We find that not only can this save a considerable amount of time
when solving least squares problems but the algorithm is also very
easy to implement.
Please use this url to cite or link to this publication:
author
Olsson, Oscar LU and Ivarsson, Tommy LU
supervisor
organization
course
FMN820 20141
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master’s Theses in Mathematical Sciences
report number
LUTFMA-3027-2014
ISSN
1404-6342
other publication id
2014:E21
language
English
id
4463318
date added to LUP
2014-06-26 11:47:56
date last changed
2015-12-14 13:32:15
@misc{4463318,
  abstract     = {In this paper we study how to update the solution of the linear
system Ax = b after the matrix A is changed by addition or deletion
of rows or columns.
Studying the QR Factorization of the system, more specifically, the
factorization created by the Householder reflection algorithm, we find
that we can split the algorithm in two parts. The result from the first
part is trivial to update and is the only dependency for calculating
the second part.
We find that not only can this save a considerable amount of time
when solving least squares problems but the algorithm is also very
easy to implement.},
  author       = {Olsson, Oscar and Ivarsson, Tommy},
  issn         = {1404-6342},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master’s Theses in Mathematical Sciences},
  title        = {Using the QR Factorization to swiftly update least squares problems},
  year         = {2014},
}