Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations

Aliyu Bhar Kisabo; Aliyu Adebimpe Funmilayo; Major Kwentoh Augustine Okey

doi:doi:10.11648/j.ijssam.20160104.13

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Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations

Aliyu Bhar Kisabo, Aliyu Adebimpe Funmilayo, Major Kwentoh Augustine Okey

Published in International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 4)

Received: 28 September 2016 Accepted: 9 October 2016 Published: 31 October 2016

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Abstract

In engineering and science, linear systems of algebraic equations occur often as exact or approximate formulations of various problems. These types of equations are well represented in matrix form. A major challenge for researchers is the choice of algorithm to use for an appropriate solution. In this study, we choose to experiment with three algorithms for the solution to a system of linear algebraic equation. After subjecting the matrix form of the system of linear algebraic equations to the rank test, Gaussian Elimination method, Inverse Matrix Method and Row-Reduced Echelon were used to evaluate twenty-four (24) sets of solutions. Numerical methods are plagued by truncation and round-off errors thus, we choose to compute and compare result here by invoking the MATLAB command format long (15 decimal place) with format short (5 decimal place). After evaluating the required solutions, we substituted all computed results back into the system of linear algebraic equations to check if they are satisfied. Comparison of results was done on the basis of algorithm used and between the results obtained using either format long or format short values. Despite the presence of errors due to truncation and round-off, format short computed solutions gave acceptable result in some cases. Results obtained in this study proved the efficacy of the proposed technique.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 4)
DOI	10.11648/j.ijssam.20160104.13
Page(s)	50-57
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Linear System of Algebraic Equations, Numerical Methods, MATLAB ^®

References

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[2]	David C. Lay, Steven R. Lay and Judi J. McDonald (2016). Linear Algebra and Its Applications, Fifth Edition. ISBN 978-0-321-98238-4.
[3]	David Poole (2011). Linear Algebra: A Modern Introduction. ISBN-13: 978-0-538-73545-2.
[4]	W. D Wallis (2012). A Beginners Guide to Finite Mathematics. ISBN 978-0-8176-8319-1.
[5]	Boege W et al (1986). Some Examples for Solving Systems of Algebraic Equations by Calculating Groebner Bases. University of Heidelberg, Institute for Applied Mathematics, Heidelberg, F.R.G. J. Symbolic Computation (1986) 1, 83-98.
[6]	Sohail A. Dianat and Eli S. Saber (2009). Advance Linear Algebra for Engineers with MATLAB. ISBN 13: 978-1-4200-9524-1.
[7]	Warren E. Stewart and Michael Caracotsios (2008). Computer-Aided Modeling of Reactive Systems. Copyright John Wiley & Sons, Inc.
[8]	Kenneth Hoffman and Ray Kunze (1971). Linear Algebra. Prentice-Hall, Inc.
[9]	William J. Palms III (2008). A Concise Introduction to MATLAB. ISBN 9780073385839.
[10]	Gilbert Strang (2005). Linear Algebra and Its Application. 4e, ISBN 13: 9780030105678.
[11]	Nicholas Loehr (2014). Advance Linear Algebra. ISBN-13: 978-1-4665-5902-8.
[12]	César Pérez López (2014). MATLAB Matrix Algebra. ISBN-13: 978-1-4842-0307-1.

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APA Style

Aliyu Bhar Kisabo, Aliyu Adebimpe Funmilayo, Major Kwentoh Augustine Okey. (2016). Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations. International Journal of Systems Science and Applied Mathematics, 1(4), 50-57. https://doi.org/10.11648/j.ijssam.20160104.13

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ACS Style

Aliyu Bhar Kisabo; Aliyu Adebimpe Funmilayo; Major Kwentoh Augustine Okey. Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations. Int. J. Syst. Sci. Appl. Math. 2016, 1(4), 50-57. doi: 10.11648/j.ijssam.20160104.13

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AMA Style

Aliyu Bhar Kisabo, Aliyu Adebimpe Funmilayo, Major Kwentoh Augustine Okey. Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations. Int J Syst Sci Appl Math. 2016;1(4):50-57. doi: 10.11648/j.ijssam.20160104.13

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@article{10.11648/j.ijssam.20160104.13,
  author = {Aliyu Bhar Kisabo and Aliyu Adebimpe Funmilayo and Major Kwentoh Augustine Okey},
  title = {Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {1},
  number = {4},
  pages = {50-57},
  doi = {10.11648/j.ijssam.20160104.13},
  url = {https://doi.org/10.11648/j.ijssam.20160104.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20160104.13},
  abstract = {In engineering and science, linear systems of algebraic equations occur often as exact or approximate formulations of various problems. These types of equations are well represented in matrix form. A major challenge for researchers is the choice of algorithm to use for an appropriate solution. In this study, we choose to experiment with three algorithms for the solution to a system of linear algebraic equation. After subjecting the matrix form of the system of linear algebraic equations to the rank test, Gaussian Elimination method, Inverse Matrix Method and Row-Reduced Echelon were used to evaluate twenty-four (24) sets of solutions. Numerical methods are plagued by truncation and round-off errors thus, we choose to compute and compare result here by invoking the MATLAB command format long (15 decimal place) with format short (5 decimal place). After evaluating the required solutions, we substituted all computed results back into the system of linear algebraic equations to check if they are satisfied. Comparison of results was done on the basis of algorithm used and between the results obtained using either format long or format short values. Despite the presence of errors due to truncation and round-off, format short computed solutions gave acceptable result in some cases. Results obtained in this study proved the efficacy of the proposed technique.},
 year = {2016}
}

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TY  - JOUR
T1  - Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations
AU  - Aliyu Bhar Kisabo
AU  - Aliyu Adebimpe Funmilayo
AU  - Major Kwentoh Augustine Okey
Y1  - 2016/10/31
PY  - 2016
N1  - https://doi.org/10.11648/j.ijssam.20160104.13
DO  - 10.11648/j.ijssam.20160104.13
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 50
EP  - 57
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20160104.13
AB  - In engineering and science, linear systems of algebraic equations occur often as exact or approximate formulations of various problems. These types of equations are well represented in matrix form. A major challenge for researchers is the choice of algorithm to use for an appropriate solution. In this study, we choose to experiment with three algorithms for the solution to a system of linear algebraic equation. After subjecting the matrix form of the system of linear algebraic equations to the rank test, Gaussian Elimination method, Inverse Matrix Method and Row-Reduced Echelon were used to evaluate twenty-four (24) sets of solutions. Numerical methods are plagued by truncation and round-off errors thus, we choose to compute and compare result here by invoking the MATLAB command format long (15 decimal place) with format short (5 decimal place). After evaluating the required solutions, we substituted all computed results back into the system of linear algebraic equations to check if they are satisfied. Comparison of results was done on the basis of algorithm used and between the results obtained using either format long or format short values. Despite the presence of errors due to truncation and round-off, format short computed solutions gave acceptable result in some cases. Results obtained in this study proved the efficacy of the proposed technique.
VL  - 1
IS  - 4
ER  -

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Author Information

Aliyu Bhar Kisabo

Center for Space Transport & Propulsion, Instrumentation & Control Department Epe, Nigeria
Aliyu Adebimpe Funmilayo

Center for Space Transport & Propulsion, Instrumentation & Control Department Epe, Nigeria
Major Kwentoh Augustine Okey

Hedquarters Nigerian Army Corps of Electrical and Mechanical Engineers Bonny Cantonment VI, Nigeria

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APA Style

Aliyu Bhar Kisabo, Aliyu Adebimpe Funmilayo, Major Kwentoh Augustine Okey. (2016). Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations. International Journal of Systems Science and Applied Mathematics, 1(4), 50-57. https://doi.org/10.11648/j.ijssam.20160104.13

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ACS Style

Aliyu Bhar Kisabo; Aliyu Adebimpe Funmilayo; Major Kwentoh Augustine Okey. Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations. Int. J. Syst. Sci. Appl. Math. 2016, 1(4), 50-57. doi: 10.11648/j.ijssam.20160104.13

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AMA Style

Aliyu Bhar Kisabo, Aliyu Adebimpe Funmilayo, Major Kwentoh Augustine Okey. Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations. Int J Syst Sci Appl Math. 2016;1(4):50-57. doi: 10.11648/j.ijssam.20160104.13

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@article{10.11648/j.ijssam.20160104.13,
  author = {Aliyu Bhar Kisabo and Aliyu Adebimpe Funmilayo and Major Kwentoh Augustine Okey},
  title = {Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {1},
  number = {4},
  pages = {50-57},
  doi = {10.11648/j.ijssam.20160104.13},
  url = {https://doi.org/10.11648/j.ijssam.20160104.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20160104.13},
  abstract = {In engineering and science, linear systems of algebraic equations occur often as exact or approximate formulations of various problems. These types of equations are well represented in matrix form. A major challenge for researchers is the choice of algorithm to use for an appropriate solution. In this study, we choose to experiment with three algorithms for the solution to a system of linear algebraic equation. After subjecting the matrix form of the system of linear algebraic equations to the rank test, Gaussian Elimination method, Inverse Matrix Method and Row-Reduced Echelon were used to evaluate twenty-four (24) sets of solutions. Numerical methods are plagued by truncation and round-off errors thus, we choose to compute and compare result here by invoking the MATLAB command format long (15 decimal place) with format short (5 decimal place). After evaluating the required solutions, we substituted all computed results back into the system of linear algebraic equations to check if they are satisfied. Comparison of results was done on the basis of algorithm used and between the results obtained using either format long or format short values. Despite the presence of errors due to truncation and round-off, format short computed solutions gave acceptable result in some cases. Results obtained in this study proved the efficacy of the proposed technique.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations
AU  - Aliyu Bhar Kisabo
AU  - Aliyu Adebimpe Funmilayo
AU  - Major Kwentoh Augustine Okey
Y1  - 2016/10/31
PY  - 2016
N1  - https://doi.org/10.11648/j.ijssam.20160104.13
DO  - 10.11648/j.ijssam.20160104.13
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 50
EP  - 57
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20160104.13
AB  - In engineering and science, linear systems of algebraic equations occur often as exact or approximate formulations of various problems. These types of equations are well represented in matrix form. A major challenge for researchers is the choice of algorithm to use for an appropriate solution. In this study, we choose to experiment with three algorithms for the solution to a system of linear algebraic equation. After subjecting the matrix form of the system of linear algebraic equations to the rank test, Gaussian Elimination method, Inverse Matrix Method and Row-Reduced Echelon were used to evaluate twenty-four (24) sets of solutions. Numerical methods are plagued by truncation and round-off errors thus, we choose to compute and compare result here by invoking the MATLAB command format long (15 decimal place) with format short (5 decimal place). After evaluating the required solutions, we substituted all computed results back into the system of linear algebraic equations to check if they are satisfied. Comparison of results was done on the basis of algorithm used and between the results obtained using either format long or format short values. Despite the presence of errors due to truncation and round-off, format short computed solutions gave acceptable result in some cases. Results obtained in this study proved the efficacy of the proposed technique.
VL  - 1
IS  - 4
ER  -

Copy | Download