메뉴 건너뛰기




Volumn 58, Issue 4, 2011, Pages 513-527

Accurate fourteenth-order methods for solving nonlinear equations

Author keywords

Efficiency index; Four step methods; Nonlinear equations; Order of convergence; Simple root; Three step methods

Indexed keywords


EID: 80855138739     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-011-9467-4     Document Type: Article
Times cited : (34)

References (19)
  • 1
    • 35448976006 scopus 로고    scopus 로고
    • Some sixth-order variants of Ostrowski root finding methods
    • Chun, C., Ham, Y.: Some sixth-order variants of Ostrowski root finding methods. Appl. Math. Comput. 193, 389-394 (2007).
    • (2007) Appl. Math. Comput. , vol.193 , pp. 389-394
    • Chun, C.1    Ham, Y.2
  • 2
    • 77950459802 scopus 로고    scopus 로고
    • Efficient three-step iterative methods with sixth order convergence for nonlinear equations
    • Cordero, A., Hueso, J. L., Martinez, M., Torregrosa, J. R.: Efficient three-step iterative methods with sixth order convergence for nonlinear equations. Numer. Algorithms 53, 485-495 (2010).
    • (2010) Numer. Algorithms , vol.53 , pp. 485-495
    • Cordero, A.1    Hueso, J.L.2    Martinez, M.3    Torregrosa, J.R.4
  • 3
    • 0041840554 scopus 로고    scopus 로고
    • Modified Newton's method with third order convergence and multiple roots
    • Frontini, M., Sormani, E.: Modified Newton's method with third order convergence and multiple roots. J. Comput. Appl. Math. 156, 345-354 (2003).
    • (2003) J. Comput. Appl. Math. , vol.156 , pp. 345-354
    • Frontini, M.1    Sormani, E.2
  • 4
    • 77952107147 scopus 로고    scopus 로고
    • A study of accelerated Newton methods for multiple polynomial roots
    • Galantai, A., Hegedus, C. J.: A study of accelerated Newton methods for multiple polynomial roots. Numer. Algorithms 54, 219-243 (2010).
    • (2010) Numer. Algorithms , vol.54 , pp. 219-243
    • Galantai, A.1    Hegedus, C.J.2
  • 5
    • 71649108856 scopus 로고    scopus 로고
    • A multi-parameter family of three-step eighth-order iterative methods locating a simple root
    • Geum, Y. H., Kim, Y. I.: A multi-parameter family of three-step eighth-order iterative methods locating a simple root. Appl. Math. Comput. 215, 3375-3382 (2010).
    • (2010) Appl. Math. Comput. , vol.215 , pp. 3375-3382
    • Geum, Y.H.1    Kim, Y.I.2
  • 6
    • 67949094317 scopus 로고    scopus 로고
    • Improving order and efficiency: composition with a modified Newton's method
    • Grau-Sanchez, M.: Improving order and efficiency: composition with a modified Newton's method. J. Comput. Appl. Math. 231, 592-597 (2009).
    • (2009) J. Comput. Appl. Math. , vol.231 , pp. 592-597
    • Grau-Sanchez, M.1
  • 7
    • 46749089996 scopus 로고    scopus 로고
    • On new third-order convergent iterative formulas
    • Haijun, W.: On new third-order convergent iterative formulas. Numer. Algorithms 48, 317-325 (2008).
    • (2008) Numer. Algorithms , vol.48 , pp. 317-325
    • Haijun, W.1
  • 8
    • 33947709556 scopus 로고    scopus 로고
    • A family of fifth-order iterations composed of Newton and third-order methods
    • Kou, J., Li, Y., Wang, X.: A family of fifth-order iterations composed of Newton and third-order methods. Appl. Math. Comput. 186, 1258-1262 (2007).
    • (2007) Appl. Math. Comput. , vol.186 , pp. 1258-1262
    • Kou, J.1    Li, Y.2    Wang, X.3
  • 9
    • 0016115525 scopus 로고
    • Optimal order of one-point and multipoint iteration
    • Kung, H. T., Traub, J. F.: Optimal order of one-point and multipoint iteration. J. Assoc. Comput. Math. 21, 643-651 (1974).
    • (1974) J. Assoc. Comput. Math. , vol.21 , pp. 643-651
    • Kung, H.T.1    Traub, J.F.2
  • 10
    • 78751627069 scopus 로고    scopus 로고
    • A note on the constructing of nonstationary methods for solving nonlinear equations with raised speed of convergence
    • Kyurkchiev, N., Iliev, A.: A note on the constructing of nonstationary methods for solving nonlinear equations with raised speed of convergence. Serdica J. Comput. 3, 47-74 (2009).
    • (2009) Serdica J. Comput. , vol.3 , pp. 47-74
    • Kyurkchiev, N.1    Iliev, A.2
  • 11
    • 0002995940 scopus 로고
    • Error analysis for the Newton-Raphson method
    • Lancaster, P.: Error analysis for the Newton-Raphson method. Numer. Math. 9, 55-68 (1966).
    • (1966) Numer. Math. , vol.9 , pp. 55-68
    • Lancaster, P.1
  • 12
    • 77649128052 scopus 로고    scopus 로고
    • On a general class of multipoint root-finding methods of high computational efficiency
    • Petkovic, M. S.: On a general class of multipoint root-finding methods of high computational efficiency. SIAM J. Numer. Anal. 47, 4402-4414 (2010).
    • (2010) SIAM J. Numer. Anal. , vol.47 , pp. 4402-4414
    • Petkovic, M.S.1
  • 14
    • 77954459261 scopus 로고    scopus 로고
    • A new family of modified Ostrowski's methods with accelerated eighth order convergence
    • Sharma, J. R., Sharma, R.: A new family of modified Ostrowski's methods with accelerated eighth order convergence. Numer. Algorithms 54, 445-458 (2010).
    • (2010) Numer. Algorithms , vol.54 , pp. 445-458
    • Sharma, J.R.1    Sharma, R.2
  • 16
    • 70349484413 scopus 로고    scopus 로고
    • Modified Jarratt method with sixth-order convergence
    • Wang, X., Kou, J., Li, Y.: Modified Jarratt method with sixth-order convergence. Appl. Math. Lett. 22, 1798-1802 (2009).
    • (2009) Appl. Math. Lett. , vol.22 , pp. 1798-1802
    • Wang, X.1    Kou, J.2    Li, Y.3
  • 17
    • 77949484764 scopus 로고    scopus 로고
    • Modified Ostrowski's method with eighth-order convergence and high efficiency index
    • Wang, X., Liu, L.: Modified Ostrowski's method with eighth-order convergence and high efficiency index. Appl. Math. Lett. 23, 549-554 (2010).
    • (2010) Appl. Math. Lett. , vol.23 , pp. 549-554
    • Wang, X.1    Liu, L.2
  • 18
    • 0012466757 scopus 로고    scopus 로고
    • A variant of Newton's method with accelerated third-order convergence
    • Weerakoon, S., Fernando, T. G. I.: A variant of Newton's method with accelerated third-order convergence. Appl. Math. Lett. 13, 87-93 (2000).
    • (2000) Appl. Math. Lett. , vol.13 , pp. 87-93
    • Weerakoon, S.1    Fernando, T.G.I.2
  • 19
    • 76149103883 scopus 로고    scopus 로고
    • Iterative methods based on the Signum function approach for solving nonlinear equations
    • Yun, B. I., Petkovic, M. S.: Iterative methods based on the Signum function approach for solving nonlinear equations. Numer. Algorithms 52, 649-662 (2009).
    • (2009) Numer. Algorithms , vol.52 , pp. 649-662
    • Yun, B.I.1    Petkovic, M.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.