Notes on Pseudoinverses : Application to Identification
(1970) In Research Reports TFRT-3021- Abstract
- In this report we will discuss the possibilities of defining a "good solution" of a system of linear equations.
Ax=b 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.
The concepts of the least squares problem are applied to identification of a linear time-invariant, discrete, single input, single output system. Some... (More) - In this report we will discuss the possibilities of defining a "good solution" of a system of linear equations.
Ax=b 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.
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.
The results in chapter 10 and the last half of chapter 11 are believed to be new. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8601127
- author
- Söderström, Torsten
- organization
- publishing date
- 1970
- type
- Book/Report
- publication status
- published
- subject
- in
- Research Reports TFRT-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
- 2016-04-01 16:30:03
- date last changed
- 2018-11-21 20:41:52
@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. <br/><br/> Ax=b 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/><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.}},
author = {{Söderström, Torsten}},
institution = {{Department of Automatic Control, Lund Institute of Technology (LTH)}},
issn = {{0346-5500}},
language = {{eng}},
series = {{Research Reports TFRT-3021}},
title = {{Notes on Pseudoinverses : Application to Identification}},
url = {{https://lup.lub.lu.se/search/files/4691638/8625796.pdf}},
year = {{1970}},
}