Journal ArticleDOI
A steffensen-type method for computing a root
L. E. Garey,R. E. Shaw +1 more
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In this article, a modification of a Steffensen-type procedure is used to find a simple root of an equation, which produces two sequences of iterates, each of which converge to the root from opposite sides.Abstract:
In this paper a modification of a Steffensen-type procedure is used to find a simple root of an equation. The modified algorithm produces two sequences of iterates, each of which converge to the root from opposite sides. The method is illustrated using two numerical examples.read more
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Book ChapterDOI
Bisection and Interpolation Methods
J.M. McNamee,Victor Y. Pan +1 more
TL;DR: In this paper, the secant method is extended to include the bisection method, where a or b is replaced by c according to the sign of f ( c ) as in the Regula Falsi method.
Journal ArticleDOI
A new cubic method for computing a root
R. E. Shaw,L. E. Garey +1 more
TL;DR: A hybrid procedure that combines Newton's quadratic root finding method with a superlinear method to find a simple root in an interval I of f(x)=0 where the function is convex is introduced.
References
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Journal ArticleDOI
The “Pegasus” method for computing the root of an equation
TL;DR: In this article, a modified Regula Falsi method is described which is appropriate for use when an interval bracketing of the root is known, and the algorithm appears to exhibit superior asymptotic convergence properties to other modified linear methods.
Journal ArticleDOI
Monotone Enclosing of Solutions of the Steffensen-type
TL;DR: In this paper, the authors consider two iterative methods of the Steffensen type, and show two enclosing theorems and establish orders of convergence for the two methods with order two and three.