Rational Arithmetic as a Means of Matrix Inversion
The solution to a set of simultaneous equations is of the form A-1 B = X where A-1 is the inverse of A in the equation AX= B. The purpose of this study is to obtain an exact A-1 through the use of rational arithmetic, and to study the behavior of rational numbers when used in arithmetic calculations...
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ndltd-UTAHS-oai-digitalcommons.usu.edu-etd-78782019-10-13T06:07:59Z Rational Arithmetic as a Means of Matrix Inversion Peterson, Jay Roland The solution to a set of simultaneous equations is of the form A-1 B = X where A-1 is the inverse of A in the equation AX= B. The purpose of this study is to obtain an exact A-1 through the use of rational arithmetic, and to study the behavior of rational numbers when used in arithmetic calculations. This study describes a matrix inversion program written in SPS II, utilizing the concept of rational arithmetic. This program, using the Gaussian elimination matrix inversion method, is compared to the same method written in Fortran. Gaussian elimination was used by this study because of its simplicity and speed of inversion. The Adjoint method was ruled out because of its complexity and relative lack of speed when compared with Gaussian elimination. The Fortran program gives only an approximate inverse due to the rounding error while the rational arithmetic program gives an exact inverse. 1967-05-01T07:00:00Z text application/pdf https://digitalcommons.usu.edu/etd/6815 https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=7878&context=etd Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact digitalcommons@usu.edu. All Graduate Theses and Dissertations DigitalCommons@USU matrix inversion rational arithmetic fortran matrix inversion Computer Sciences Statistics and Probability |
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matrix inversion rational arithmetic fortran matrix inversion Computer Sciences Statistics and Probability |
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matrix inversion rational arithmetic fortran matrix inversion Computer Sciences Statistics and Probability Peterson, Jay Roland Rational Arithmetic as a Means of Matrix Inversion |
description |
The solution to a set of simultaneous equations is of the form A-1 B = X where A-1 is the inverse of A in the equation AX= B. The purpose of this study is to obtain an exact A-1 through the use of rational arithmetic, and to study the behavior of rational numbers when used in arithmetic calculations.
This study describes a matrix inversion program written in SPS II, utilizing the concept of rational arithmetic. This program, using the Gaussian elimination matrix inversion method, is compared to the same method written in Fortran. Gaussian elimination was used by this study because of its simplicity and speed of inversion. The Adjoint method was ruled out because of its complexity and relative lack of speed when compared with Gaussian elimination.
The Fortran program gives only an approximate inverse due to the rounding error while the rational arithmetic program gives an exact inverse. |
author |
Peterson, Jay Roland |
author_facet |
Peterson, Jay Roland |
author_sort |
Peterson, Jay Roland |
title |
Rational Arithmetic as a Means of Matrix Inversion |
title_short |
Rational Arithmetic as a Means of Matrix Inversion |
title_full |
Rational Arithmetic as a Means of Matrix Inversion |
title_fullStr |
Rational Arithmetic as a Means of Matrix Inversion |
title_full_unstemmed |
Rational Arithmetic as a Means of Matrix Inversion |
title_sort |
rational arithmetic as a means of matrix inversion |
publisher |
DigitalCommons@USU |
publishDate |
1967 |
url |
https://digitalcommons.usu.edu/etd/6815 https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=7878&context=etd |
work_keys_str_mv |
AT petersonjayroland rationalarithmeticasameansofmatrixinversion |
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