Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations

Nasr Al Din Ide

doi:doi:10.11648/j.ijtam.20160202.31

| Peer-Reviewed

Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations

Nasr Al Din Ide

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)

Received: 14 November 2016 Accepted: 12 December 2016 Published: 22 January 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Finding the roots of nonlinear algebraic equations is an important problem in science and engineering, later many methods developed for solving nonlinear equations. These methods are given [1-28], in this paper, a new Algorithm for solving nonlinear algebraic equations is obtained by using Lagrange Interpolation method by fitting a polynomial form of degree two. This paper compare the present method with the Famous methods of Regula Falsi (RF), Besection (BS), Modified Regula Falsi (MRF), Nonlinear Regression Method (NR) given by Jutaporn N, Bumrungsak P and Apichat N, 2016 [1] and Least Square Method (LS) given by N. IDE, 2016 [2]. We verified on a number of examples and numerical results obtained show that the present method is faster than the other methods.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.ijtam.20160202.31
Page(s)	165-169
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), 2017. Published by Science Publishing Group

Keywords

Nonlinear Algebraic Equations, Least Square Method, Lagrange Interpolation Method, Nonlinear Regression Method

References

[1]	Jutaporn N, Bumrungsak P and Apichat N, A new method for finding Root of Nonlinear Equations by using Nonlinear Regression, Asian Journal of Applied Sciences, Vol 03-Issue 06, 2015: 818-822.
[2]	A New Algorithm for Solving Nonlinear Equations by Using Least Square Method, Mathematics and Computer Science, Science Publishing Group, Vol 1, Issue 3, September 2016, Pages: 44-47, 2016.
[3]	J. F. Traub, “Iterative Methods for the Solution of Equations”, Prentice Hall, Englewood Cliffs, N. J., 1964.
[4]	Neamvonk A., “A Modified Regula Falsi Method for Solving Root of Nonlinear Equations”, Asian Journal of Applied Sciences, vol. 3, no. 4, pp. 776-778, 2015.
[5]	N. Ide, (2008). A new Hybrid iteration method for solving algebraic equations, Journal of Applied Mathematics and Computation, Elsevier Editorial, Amsterdam, 195, Netherlands, 772-774.
[6]	N. Ide, (2008). On modified Newton methods for solving a nonlinear algebraic equations, Journal of Applied Mathematics and Computation, Elsevier Editorial, Amsterdam, Netherlands.
[7]	N. Ide, (2013). Some New Type Iterative Methods for Solving Nonlinear Algebraic Equation", World applied sciences journal, 26 (10); 1330-1334, 2013.
[8]	M. Javidi, 2007, Iterative Method to Nonlinear Equations, Journal of Applied Mathematics and Computation, Elsevier Editorial, Amsterdam, 193, Netherlands, 360-365.
[9]	J. H. He (2003). A new iterative method for solving algebraic equations. Appl. Math. Comput. 135: 81-84.
[10]	M. Javidi, (2009). Fourth-order and fifth-order iterative methods for nonlinear algebraic equations. Math. Comput. Model. 50: 66-71.
[11]	M. Basto M, V. Semiao, FL. Calheiros (2006). A new iterative method to compute nonlinear equations. Appl. Math. Comput. 173: 468-483.
[12]	C. Chun (2006). A new iterative method for solving nonlinear equations. Appl. Math. Comput. 178: 415-422.
[13]	MA. Noor (2007). New family of iterative methods for nonlinear equations. Appl. Math. Compute. 190: 553-558.
[14]	MA. Noor, KI. Noor, ST. Mohyud-Din, A. Shabbir, (2006). An iterative method with cubic convergence for nonlinear equations. Appl. Math. Comput. 183: 1249-1255.
[15]	W. Bi, H. Ren, Q. Wu (2009). Three-step iterative methods with eighth-order convergence for solving nonlinear equations. J. Comput. Appl. Math. 225: 105-112.
[16]	W. Bi, H. Ren, Q. Wu (2009). A new family of eighth-order iterative methods for solving nonlinear equations. Appl. Math. Comput. 214: 236-245.
[17]	K. Jisheng, L. Yitian, W. Xiuhua (2007). A composite fourth-order iterative method for solving non-linear equations. Appl. Math. Comput. 184: 471-475.
[18]	N. IDE Some New Iterative Algorithms by Using Homotopy Perturbation Method for Solving Nonlinear Algebraic Equations, 2015, Asian Journal of Mathematics and Computer Research, (AJOMCOR), International Knowledge Press, Vol. 5, Issue 3, 2015.
[19]	C. Chun, Construction of Newton-like iteration methods for solving nonlinear equations, Numerical Mathematics 104, (2006), 297-315.
[20]	M. Frontini, and E. Sormani, Some variant of Newton's method with third-order convergence, Applied Mathematics and Computation 140, (2003), 419-426.
[21]	M. Frontini, and E. Sormani, Third-order methods from quadrature formulae for solving systems of nonlinear equations, Applied Mathematics and Computation 149, (2004), 771-782.
[22]	J. H. He, Newton-like iteration method for solving algebraic equations, Communications on Nonlinear Science and Numerical Simulation 3, (1998) 106-109.
[23]	H. H. H. Homeier, A modified Newton method with cubic convergence: the multivariate case, Journal of Computational and Applied Mathematics 169, (2004), 161-169.
[24]	H. H. H. Homeier, On Newton-type methods with cubic convergence, Journal of Computational and Applied Mathematics 176, (2005), 425-432.
[25]	J. Kou, Y. Li, and X. Wang, A modification of Newton method with third-order convergence, Applied Mathematics and Computation 181, (2006), 1106-1111.
[26]	A. Y. Ozban, Some new variants of Newton's method, Applied Mathematics Letters 17, (2004), 677-682.
[27]	J. F. Traub, Iterative Methods for the Solution of Equations, Chelsea Publishing Company, New York, 1982.
[28]	S. Weerakoon, and G. I. Fernando, A variant of Newton's method with accelerated third-order convergence, Applied Mathematics Letters 17, (2000), 87-93.

Cite This Article

Plain Text BibTeX RIS

APA Style

Nasr Al Din Ide. (2017). Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations. International Journal of Theoretical and Applied Mathematics, 2(2), 165-169. https://doi.org/10.11648/j.ijtam.20160202.31

Copy | Download

ACS Style

Nasr Al Din Ide. Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations. Int. J. Theor. Appl. Math. 2017, 2(2), 165-169. doi: 10.11648/j.ijtam.20160202.31

Copy | Download

AMA Style

Nasr Al Din Ide. Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations. Int J Theor Appl Math. 2017;2(2):165-169. doi: 10.11648/j.ijtam.20160202.31

Copy | Download

@article{10.11648/j.ijtam.20160202.31,
  author = {Nasr Al Din Ide},
  title = {Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {165-169},
  doi = {10.11648/j.ijtam.20160202.31},
  url = {https://doi.org/10.11648/j.ijtam.20160202.31},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.31},
  abstract = {Finding the roots of nonlinear algebraic equations is an important problem in science and engineering, later many methods developed for solving nonlinear equations. These methods are given [1-28], in this paper, a new Algorithm for solving nonlinear algebraic equations is obtained by using Lagrange Interpolation method by fitting a polynomial form of degree two. This paper compare the present method with the Famous methods of Regula Falsi (RF), Besection (BS), Modified Regula Falsi (MRF), Nonlinear Regression Method (NR) given by Jutaporn N, Bumrungsak P and Apichat N, 2016 [1] and Least Square Method (LS) given by N. IDE, 2016 [2]. We verified on a number of examples and numerical results obtained show that the present method is faster than the other methods.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations
AU  - Nasr Al Din Ide
Y1  - 2017/01/22
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20160202.31
DO  - 10.11648/j.ijtam.20160202.31
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 165
EP  - 169
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160202.31
AB  - Finding the roots of nonlinear algebraic equations is an important problem in science and engineering, later many methods developed for solving nonlinear equations. These methods are given [1-28], in this paper, a new Algorithm for solving nonlinear algebraic equations is obtained by using Lagrange Interpolation method by fitting a polynomial form of degree two. This paper compare the present method with the Famous methods of Regula Falsi (RF), Besection (BS), Modified Regula Falsi (MRF), Nonlinear Regression Method (NR) given by Jutaporn N, Bumrungsak P and Apichat N, 2016 [1] and Least Square Method (LS) given by N. IDE, 2016 [2]. We verified on a number of examples and numerical results obtained show that the present method is faster than the other methods.
VL  - 2
IS  - 2
ER  -

Copy | Download

Author Information

Nasr Al Din Ide

Faculty of Science, Department of Mathematics, Aleppo University, Aleppo, Syria

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Nasr Al Din Ide. (2017). Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations. International Journal of Theoretical and Applied Mathematics, 2(2), 165-169. https://doi.org/10.11648/j.ijtam.20160202.31

Copy | Download

ACS Style

Nasr Al Din Ide. Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations. Int. J. Theor. Appl. Math. 2017, 2(2), 165-169. doi: 10.11648/j.ijtam.20160202.31

Copy | Download

AMA Style

Nasr Al Din Ide. Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations. Int J Theor Appl Math. 2017;2(2):165-169. doi: 10.11648/j.ijtam.20160202.31

Copy | Download

@article{10.11648/j.ijtam.20160202.31,
  author = {Nasr Al Din Ide},
  title = {Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {165-169},
  doi = {10.11648/j.ijtam.20160202.31},
  url = {https://doi.org/10.11648/j.ijtam.20160202.31},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.31},
  abstract = {Finding the roots of nonlinear algebraic equations is an important problem in science and engineering, later many methods developed for solving nonlinear equations. These methods are given [1-28], in this paper, a new Algorithm for solving nonlinear algebraic equations is obtained by using Lagrange Interpolation method by fitting a polynomial form of degree two. This paper compare the present method with the Famous methods of Regula Falsi (RF), Besection (BS), Modified Regula Falsi (MRF), Nonlinear Regression Method (NR) given by Jutaporn N, Bumrungsak P and Apichat N, 2016 [1] and Least Square Method (LS) given by N. IDE, 2016 [2]. We verified on a number of examples and numerical results obtained show that the present method is faster than the other methods.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Using Lagrange Interpolation for Solving Nonlinear Algebraic Equations
AU  - Nasr Al Din Ide
Y1  - 2017/01/22
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20160202.31
DO  - 10.11648/j.ijtam.20160202.31
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 165
EP  - 169
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160202.31
AB  - Finding the roots of nonlinear algebraic equations is an important problem in science and engineering, later many methods developed for solving nonlinear equations. These methods are given [1-28], in this paper, a new Algorithm for solving nonlinear algebraic equations is obtained by using Lagrange Interpolation method by fitting a polynomial form of degree two. This paper compare the present method with the Famous methods of Regula Falsi (RF), Besection (BS), Modified Regula Falsi (MRF), Nonlinear Regression Method (NR) given by Jutaporn N, Bumrungsak P and Apichat N, 2016 [1] and Least Square Method (LS) given by N. IDE, 2016 [2]. We verified on a number of examples and numerical results obtained show that the present method is faster than the other methods.
VL  - 2
IS  - 2
ER  -

Copy | Download