AN ACCELERATION PROCEDURE OF REGULA FALSI METHOD

Main Article Content

M. A. HERNANDEZ
M. A. SALANOVA

Abstract




From the Regula Falsi method a family of iterative processes is defined. A family of accelerations is obtained, by means of a geometric procedure. From this, a family of new iterative processes with, at least, quadratic convergence is derived. A study of their convergence and optimization is done in $\mathbb{R}$ and in the complex plane. All of them are better than Newton met hod .




Article Details

How to Cite
HERNANDEZ, M. A., & SALANOVA, M. A. (1997). AN ACCELERATION PROCEDURE OF REGULA FALSI METHOD. Tamkang Journal of Mathematics, 28(1), 67–77. https://doi.org/10.5556/j.tkjm.28.1997.4336
Section
Papers

References

M. A. Hernandez, and M. A. Salanova, " A family of Newton type iterative processes," Intern. J. Computer. Math., 51(1994), 205-214.

A. S. Householder, The Numerical Treatment of a Single Nonlinear Equation, Mc Graw-Hill, 1970.

L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, 1982.

A. M. Ostrowski, Solution of Equations in Euclidean and Banach Space, Academic Press, 1973.

W. C. Rheinholdt, " A Unifed convergence theory for a Class of Iterative Process," SIAM J. Numer. Anal., 5(1968), 42-.63.