Improved Muller method and Bisection method with global and asymptotic superlinear convergence of both point and interval for solving nonlinear equations

Applied Mathematics and Computation

Volumn 166, Issue 2, 2005, Pages 299-311

  Wu, Xinyuan ^a  

^a NANJING UNIVERSITY   (China)

Author keywords

Bisection method; Convergence of interval diameter; Global convergence; Iteration method; Muller's method; Nonlinear equations; Root finding; Superlincar convergence

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; ITERATIVE METHODS; POLYNOMIALS; PROBLEM SOLVING; QUADRATIC PROGRAMMING; SET THEORY;

BISECTION METHOD; CONVERGENCE OF INTERNAL DIAMETER; GLOBAL CONVERGENCE; ITERATION METHODS; MULLER'S METHOD; ROOT FINDING; SUPERLINEAR CONVERGENCE;

NONLINEAR EQUATIONS;

EID: 19944396144     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.04.120     Document Type: Article

References (16)

1. D.E. Muller A method for solving algebraic equations using an automatic computer Math. Tables Other Aids Comput. 10 1956 208 215
2. M. Dowell, and D. Jarratt A modified regula falsi method for computing the root of an equation BIT 11 1971 168 174
3. M. Dowell, and D. Jarratt The "Pegasus" method for computing the root of an equation BIT 12 1972 503 508
4. F.K. Richard An improved Pegasus method for root finding BIT 13 1973 423 427
5. A.M. Ostrowski Solution of Equations in Euclidean and Banach Space third ed. 1973 Academic Press New York and London
6. G. Alefeld, and F.A. Potra Some efficient methods for enclosing simple zeroes of nonlinear equations BIT 32 1992 334 344
7. G. Alefeld, F.A. Potra, and Y.X. Shi On enclosing simple roots of nonlinear equations Math. Comp. 61 1993 733 744
8. R.L. Burden, and J.D. Faires Numerical Analysis third ed. 1985 PWS Publishers Chapter 2, pp. 72
9. X. Wu, Z. Shen, and J. Xia An improved regula falsi method with quadratic convergence of both diameter and point for enclosing simple zeros of nonlinear equations Appl. Math. Comput. 144 2-3 2003 381 388
10. X. Wu, and D. Fu New high order convergence iteration methods without employing derivatives for solving nonlinear equations Comput. Math. Appl. 41 2001 489 495
11. X. Wu, J. Xia, and R. Shao Quadratically convergent multiple roots finding method without derivatives Comput. Math. Appl. 42 2001 115 119
12. S.R.K. lyengar, and R.K. Jain Derivative free multipoint iterative methods for simple and multiple roots BIT 26 1986 93 99
13. J.B. Kioustelidis A derivative-free transformation preserving the order of convergence of iteration methods in case of multiple zeroes Numer. Math. 33 1979 385 389
14. F. Richard King A secant method for multiple roots BIT 17 1977 321 328
15. G.W. Stewart The behavior of a multiplicity independent root-finding scheme in the presence of error BIT 20 1980 526 528
16. X. Wu Error analysis of a new transformation for multiple zeros finding free from derivative evaluations Comput. Math. Appl. 46 8-9 2003 1195 1200