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Notes on Pseudoinverses. Application to Identification.

Söderström, Torsten (1970) In Report TFRT 3021.
Abstract
In this report we will discuss the possibilities of defining a "good solution" of a system of linear equations. <br><br> Ax=b <br><br> where A is not necessarily quadratic. Especially the least squares problem will be treated. The concepts of pseudo inverses are introduced and its application to the least squares problem is shown. Geometrical interpretation of the solution in different cases is given. Different algorithms for computing the pseudo inverse are briefly discussed. One is programmed and compared with another program, given by Golub-Reinsch. Numerical examples are given. <br> The concepts of the least squares problem are applied to identification of a linear time-invariant, discrete, single input,... (More)
In this report we will discuss the possibilities of defining a "good solution" of a system of linear equations. <br><br> Ax=b <br><br> where A is not necessarily quadratic. Especially the least squares problem will be treated. The concepts of pseudo inverses are introduced and its application to the least squares problem is shown. Geometrical interpretation of the solution in different cases is given. Different algorithms for computing the pseudo inverse are briefly discussed. One is programmed and compared with another program, given by Golub-Reinsch. Numerical examples are given. <br> The concepts of the least squares problem are applied to identification of a linear time-invariant, discrete, single input, single output system. Some recursive equations are given. The consequences of using a model of too high an order for systems with and systems without noise are discussed. <br> The results in chapter 10 and the last half of chapter 11 are believed to be new. (Less)
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author
organization
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type
Book/Report
publication status
published
subject
in
Report TFRT
volume
3021
publisher
Department of Automatic Control, Lund Institute of Technology (LTH)
ISSN
0346-5500
language
English
LU publication?
no
id
0aa36941-f11f-4b33-bab6-8716fedcc3c8 (old id 8601127)
date added to LUP
2016-02-12 09:48:33
date last changed
2016-04-16 04:26:35
@techreport{0aa36941-f11f-4b33-bab6-8716fedcc3c8,
  abstract     = {In this report we will discuss the possibilities of defining a "good solution" of a system of linear equations. &lt;br&gt;&lt;br&gt; Ax=b &lt;br&gt;&lt;br&gt; where A is not necessarily quadratic. Especially the least squares problem will be treated. The concepts of pseudo inverses are introduced and its application to the least squares problem is shown. Geometrical interpretation of the solution in different cases is given. Different algorithms for computing the pseudo inverse are briefly discussed. One is programmed and compared with another program, given by Golub-Reinsch. Numerical examples are given. &lt;br&gt; The concepts of the least squares problem are applied to identification of a linear time-invariant, discrete, single input, single output system. Some recursive equations are given. The consequences of using a model of too high an order for systems with and systems without noise are discussed. &lt;br&gt; The results in chapter 10 and the last half of chapter 11 are believed to be new.},
  author       = {Söderström, Torsten},
  institution  = {Department of Automatic Control, Lund Institute of Technology (LTH)},
  issn         = {0346-5500},
  language     = {eng},
  series       = {Report TFRT},
  title        = {Notes on Pseudoinverses. Application to Identification.},
  volume       = {3021},
  year         = {1970},
}