×

Third-order and fourth-order iterative methods for finding multiple and distinct zeros of non-linear equations. (English) Zbl 1123.65039

Summary: We point out and analyse six two-step iterative methods for finding multiple as well as distinct zeros of non-linear equations. We prove that the methods for multiple zeros have third-order convergence where as the methods for distinct zeros have fourth-order convergence. The methods calculate the multiple as well as distinct zeros with high accuracy. The numerical tests show their better performance in case of algebraic as well as non-algebraic equations.

MSC:

65H05 Numerical computation of solutions to single equations

Software:

MultRoot
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Burden, R.L.; Faires, J.D., Numerical analysis, (2001), PWS Publishing Company Boston, USA
[2] Chen, J.; Li, W., On new exponential quadratically convergent iterative formulae, Appl. math. comput., 180, 1, 242-246, (2006) · Zbl 1117.65066
[3] Chun, C., Iterative methods improving newton’s method by the decomposition method, Int. J. comp. math. appl., 50, 1559-1568, (2005) · Zbl 1086.65048
[4] Frontini, M.; Sormani, E., Some variants of newton’s method with third order convergence and multiple roots, J. comput. appl. math., 156, 345-354, (2003) · Zbl 1030.65044
[5] Frontini, M.; Sormani, E., Third order methods for quadrature formulae for solving system of non-linear equations, Appl. math. comput., 149, 771-782, (2004) · Zbl 1050.65055
[6] Mamta; Kanwar, V.; Kukreja, V.K.; Singh, S., On a class of quadratically convergent iteration formulae, Appl. math. comput., 166, 3, 633-637, (2004) · Zbl 1078.65036
[7] Mamta; Kanwar, V.; Kukreja, V.K.; Singh, S., On some third order iterative methods for solving non-linear equations, Appl. math. comput., 171, 272-280, (2005) · Zbl 1084.65051
[8] Wheatley, Gerald, Applied numerical analysis, (2003), Pearson Education Inc. · Zbl 0684.65002
[9] N.A. Mir, Naila Rafiq, Fourth order two-step iterative method for determining multiple zeros of non-linear equations, Int. J. Comput. Math., in press. · Zbl 1122.65047
[10] Ujević, N., A method for solving non-linear equations, Appl. math. comput., 174, 416-426, (2006)
[11] Traub, J.F., Iterative methods for the solution of equations, (1982), Chelsea Publishing Company New York, NY · Zbl 0472.65040
[12] Zeng, Zhonggang, Computing multiple roots of inexact polynomials, Math. comput., 74, 250, 869-903, (2004) · Zbl 1079.12007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.