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Two-Point Iterative Methods for Solving Quadratic Equations and its Applications

Yıl 2018, Cilt: 6 Sayı: 2, 66 - 80, 31.10.2018

Kalyanasundaram Madhu

https://doi.org/10.36753/mathenot.476799
Cited By: 2

Öz


Anahtar Kelimeler

Quadratic equation Two-step iterative methods Kung-Traub’s conjecture Efficiency Index Systems of equations

Kaynakça

  • [1] Ahmad, F., Comment on: On the kung-traub conjecture for iterative methods for solving quadratic equations. Algorithms, 9:30, 2016.
  • [2] Babajee, D. K. R. , Madhu, K. and Jayaraman, J., A family of higher order multi-point iterative methods based on power mean for solving nonlinear equations. Afr. Mat., 27(5):865-876, 2016.
  • [3] Babajee, D.K.R., On the kung-traub conjecture for iterative methods for solving quadratic equations. Algorithms, 9:1, 2016.
  • [4] Babajee, D.K.R., Madhu, K. and Jayaraman, J., On some improved harmonic mean newton-like methods for solving systems of nonlinear equations. Algorithms, 8:895-909, 2015.
  • [5] Babajee, D.K.R. and Madhu, K., Comparing two techniques for developing higher order two-point iterative methods for solving quadratic equations. SeMA Journal, Doi: 10.1007/s40324-018-0174-0, 2018.
  • [6] Buckmire, R., Investigations of nonstandard Mickens-type finite-difference schemes for singular boundary value problems in cylindrical or spherical coordinates. Num. Meth. P. Diff. Eqns., 19(2):380-398, 2003.
  • [7] Chun, C. and Kim, Y.I., Several new third-order iterative methods for solving nonlinear equations. Acta Appl. Math., 109:1053-1063, 2010.
  • [8] Cordero, A., Hueso, J.L., Martinez, E. and Torregrosa, J.R., Accelerated methods of order 2p for systems of nonlinear equations. J. Comp. Appl. Math., 53(4):485-495, 2010.
  • [9] Cordero, A., Hueso, J.L., Martinez, E. and Torregrosa, J.R., A modified newton-jarratt’s composition. Numer. Algor., 55:87-99, 2010.
  • [10] Cordero, A and Torregrosa, J.R., Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comp., 190:686-698, 2007.
  • [11] Darvishi, M.T. and Barati, A., Super cubic iterative methods to solve systems of nonlinear equations. Appl. Math. Comp., 188:1678-1685, 2007.
  • [12] Jarratt, P., Some efficient fourth order multipoint methods for solving equations. BIT, 9:119-124, 1969.
  • [13] Kung, H.T. and Traub, J.F., Optimal order of one-point and multipoint iteration. J. Assoc. Comput. Mach., 21(4):643-651, 1974.
  • [14] Madhu, K., Note on the kung-traub conjecture for traub-type two-point iterative methods for quadratic equations. International Journal of Advance in Mathematics, Volume 2018(2):112-118, 2018.
  • [15] Madhu, K., Some new higher order multi-point iterative methods and their applications to differential and integral equation and global positioning system. PhD thesis, Pndicherry University, June 2016.
  • [16] Madhu, K. and Jayaraman, J., Higher order methods for nonlinear equations and their basins of attraction. Mathematics, 4:22, 2016.
  • [17] Odejide, S.A. and Aregbesola, Y.A.S., A note on two dimensional Bratu problem. Kragujevac J. Math., 29:49-56, 2006.
  • [18] Ostrowski, A.M., Solutions of Equations and System of equations. Academic Press, New York, 1960.
  • [19] Petkovic, M.S., Neta, B., Petkovic, L.D. and Dzunic, J., Multipoint Methods for Solving Nonlinear Equations. Elsevier, Amsterdam, 2013.
  • [20] Sharma, J.R. and Arora, H., An efficient family of weighted-newton methods with optimal eighth order convergence. Appl. Math. Lett., 29:1-6, 2014.
  • [21] Thukral, R., New modification of newton method with third-order convergence for solving nonlinear equations of type f(0) = 0. American Journal of Computational and Applied Mathematics, 6(1):14-18,

Yıl 2018, Cilt: 6 Sayı: 2, 66 - 80, 31.10.2018

Kalyanasundaram Madhu

https://doi.org/10.36753/mathenot.476799
Cited By: 2

Öz

Kaynakça

  • [1] Ahmad, F., Comment on: On the kung-traub conjecture for iterative methods for solving quadratic equations. Algorithms, 9:30, 2016.
  • [2] Babajee, D. K. R. , Madhu, K. and Jayaraman, J., A family of higher order multi-point iterative methods based on power mean for solving nonlinear equations. Afr. Mat., 27(5):865-876, 2016.
  • [3] Babajee, D.K.R., On the kung-traub conjecture for iterative methods for solving quadratic equations. Algorithms, 9:1, 2016.
  • [4] Babajee, D.K.R., Madhu, K. and Jayaraman, J., On some improved harmonic mean newton-like methods for solving systems of nonlinear equations. Algorithms, 8:895-909, 2015.
  • [5] Babajee, D.K.R. and Madhu, K., Comparing two techniques for developing higher order two-point iterative methods for solving quadratic equations. SeMA Journal, Doi: 10.1007/s40324-018-0174-0, 2018.
  • [6] Buckmire, R., Investigations of nonstandard Mickens-type finite-difference schemes for singular boundary value problems in cylindrical or spherical coordinates. Num. Meth. P. Diff. Eqns., 19(2):380-398, 2003.
  • [7] Chun, C. and Kim, Y.I., Several new third-order iterative methods for solving nonlinear equations. Acta Appl. Math., 109:1053-1063, 2010.
  • [8] Cordero, A., Hueso, J.L., Martinez, E. and Torregrosa, J.R., Accelerated methods of order 2p for systems of nonlinear equations. J. Comp. Appl. Math., 53(4):485-495, 2010.
  • [9] Cordero, A., Hueso, J.L., Martinez, E. and Torregrosa, J.R., A modified newton-jarratt’s composition. Numer. Algor., 55:87-99, 2010.
  • [10] Cordero, A and Torregrosa, J.R., Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comp., 190:686-698, 2007.
  • [11] Darvishi, M.T. and Barati, A., Super cubic iterative methods to solve systems of nonlinear equations. Appl. Math. Comp., 188:1678-1685, 2007.
  • [12] Jarratt, P., Some efficient fourth order multipoint methods for solving equations. BIT, 9:119-124, 1969.
  • [13] Kung, H.T. and Traub, J.F., Optimal order of one-point and multipoint iteration. J. Assoc. Comput. Mach., 21(4):643-651, 1974.
  • [14] Madhu, K., Note on the kung-traub conjecture for traub-type two-point iterative methods for quadratic equations. International Journal of Advance in Mathematics, Volume 2018(2):112-118, 2018.
  • [15] Madhu, K., Some new higher order multi-point iterative methods and their applications to differential and integral equation and global positioning system. PhD thesis, Pndicherry University, June 2016.
  • [16] Madhu, K. and Jayaraman, J., Higher order methods for nonlinear equations and their basins of attraction. Mathematics, 4:22, 2016.
  • [17] Odejide, S.A. and Aregbesola, Y.A.S., A note on two dimensional Bratu problem. Kragujevac J. Math., 29:49-56, 2006.
  • [18] Ostrowski, A.M., Solutions of Equations and System of equations. Academic Press, New York, 1960.
  • [19] Petkovic, M.S., Neta, B., Petkovic, L.D. and Dzunic, J., Multipoint Methods for Solving Nonlinear Equations. Elsevier, Amsterdam, 2013.
  • [20] Sharma, J.R. and Arora, H., An efficient family of weighted-newton methods with optimal eighth order convergence. Appl. Math. Lett., 29:1-6, 2014.
  • [21] Thukral, R., New modification of newton method with third-order convergence for solving nonlinear equations of type f(0) = 0. American Journal of Computational and Applied Mathematics, 6(1):14-18,
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Kalyanasundaram Madhu 0000-0002-9328-2996

Yayımlanma Tarihi 31 Ekim 2018
Gönderilme Tarihi 12 Nisan 2018
Kabul Tarihi 24 Ekim 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 2

Kaynak Göster

APA Madhu, K. (2018). Two-Point Iterative Methods for Solving Quadratic Equations and its Applications. Mathematical Sciences and Applications E-Notes, 6(2), 66-80. https://doi.org/10.36753/mathenot.476799
AMA Madhu K. Two-Point Iterative Methods for Solving Quadratic Equations and its Applications. Math. Sci. Appl. E-Notes. Ekim 2018;6(2):66-80. doi:10.36753/mathenot.476799
Chicago Madhu, Kalyanasundaram. “Two-Point Iterative Methods for Solving Quadratic Equations and Its Applications”. Mathematical Sciences and Applications E-Notes 6, sy. 2 (Ekim 2018): 66-80. https://doi.org/10.36753/mathenot.476799.
EndNote Madhu K (01 Ekim 2018) Two-Point Iterative Methods for Solving Quadratic Equations and its Applications. Mathematical Sciences and Applications E-Notes 6 2 66–80.
IEEE K. Madhu, “Two-Point Iterative Methods for Solving Quadratic Equations and its Applications”, Math. Sci. Appl. E-Notes, c. 6, sy. 2, ss. 66–80, 2018, doi: 10.36753/mathenot.476799.
ISNAD Madhu, Kalyanasundaram. “Two-Point Iterative Methods for Solving Quadratic Equations and Its Applications”. Mathematical Sciences and Applications E-Notes 6/2 (Ekim 2018), 66-80. https://doi.org/10.36753/mathenot.476799.
JAMA Madhu K. Two-Point Iterative Methods for Solving Quadratic Equations and its Applications. Math. Sci. Appl. E-Notes. 2018;6:66–80.
MLA Madhu, Kalyanasundaram. “Two-Point Iterative Methods for Solving Quadratic Equations and Its Applications”. Mathematical Sciences and Applications E-Notes, c. 6, sy. 2, 2018, ss. 66-80, doi:10.36753/mathenot.476799.
Vancouver Madhu K. Two-Point Iterative Methods for Solving Quadratic Equations and its Applications. Math. Sci. Appl. E-Notes. 2018;6(2):66-80.

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https://doi.org/10.1080/09720502.2021.1884393

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