Three new rapidly convergent algorithms for finding a zero of a function. (English) Zbl 0561.65033

Le, D.

SIAM J. Sci. Stat. Comput. 6, 193-208 (1985).

The paper is concerned with three algorithms using only function evaluations for finding a zero of a nonlinear function of a single variable. The algorithms are three-step methods. Three approximations of the solution are iteratively improved. The methods combine bisections with linear, quadratic, and cushion interpolation. The paper contains many numerical results and includes comparisons with known algorithms. (There is an interesting argument in the text: It is not reasonable to start with the regula falsi and skip to bisection if poor convergence is observed. During early iterations, the interval is often very large and thus may contain irregularities which make a superlinear convergent method very inefficient, and the change to other methods may be too late).

Reviewer: D.Braess

MSC:

65H05

Numerical computation of solutions to single equations

Keywords:

zero finding; iterative methods; three-step methods; bisections; cushion interpolation; numerical results; comparisons; convergence