Results 1 to 10 of about 93,385 (159)
Computing Simple Roots by an Optimal Sixteenth-Order Class [PDF]
Journal of Applied Mathematics, 2012 The problem considered in this paper is to approximate the simple zeros of the function by iterative processes. An optimal 16th order class is constructed.
F. Soleymani, S. Shateyi, H. Salmani
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A parallel algorithm for simple roots for polynomials
Computers and Mathematics With Applications, 1984 An algorithm for the simultaneous finding of simple roots is presented. It is based on the theory of divided differences. The most time-consuming parts can run in parallel on a SIMD computer (and thus also on a vector computer). The method compares favorably to Laguerre's and to Jenkins- Traub's method.
Layne Watson
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Simple algorithms for approximating all roots of a polynomial with real roots
Journal of Complexity, 1990 Let p be a polynomial of degree n in \({\mathbb{Z}}[x]\) with n distinct real roots. Suppose that the coefficients of p are all in absolute value less than \(2^ m\). It is shown that the approximation of all roots of p, within precision \(2^{-\mu}\) is P-uniform \(NC^ 2\) and it can be solved by a sequential algorithm using only \(O(n^ 2(m+\mu)\log^ 6 ...
Michael Ben-Or
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Basin attractors for derivative-free methods to find simple roots of nonlinear equations
Journal of Numerical Analysis and Approximation Theory, 2020 Many methods exist for solving nonlinear equations. Several of these methods are derivative-free. One of the oldest is the secant method where the derivative is replaced by a divided difference.
Beny Neta
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A New Derivative-Free Method to Solve Nonlinear Equations
Mathematics, 2021 A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty is the use of Traub’s method as a first step. The order is proven and demonstrated.
Beny Neta
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Basins of attraction for family of Popovski’s methods and their extension to multiple roots
Journal of Numerical Analysis and Approximation Theory, 2022 In this paper we revisit Popovski’s family of methods for simple roots. We compare several members using basins of attraction visually and qualitatively by comparing the run-time on several examples, the average number of iterations and the number of ...
Beny Neta
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A simple and efficient protocol for generating transgenic hairy roots using Agrobacterium rhizogenes
PLoS ONE, 2023 For decades, Agrobacterium rhizogenes (now Rhizobium rhizogenes), the causative agent of hairy root disease, has been harnessed as an interkingdom DNA delivery tool for generating transgenic hairy roots on a wide variety of plants.
Shaun Ferguson +7 more
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ON THE ROOTS OF SYSTEMS OF TRANSCENDENTAL EQUATIONS
Проблемы анализа, 2023 The article is devoted to investigation of simple and multiple roots of systems of transcendental equations. It is shown that the number is related to the number of real roots of the resultant of the system. Examples for systems of equations are given.
A. M. Kytmanov, O. V. Khodos
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Results in Control and Optimization, 2023 We present in this paper two new families of bi-parametric multipoint higher order iterative methods of optimal order for determining simple roots of the nonlinear equation Ω(s)=0.
G Thangkhenpau +2 more
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A New Newton Method with Memory for Solving Nonlinear Equations
Mathematics, 2020 A new Newton method with memory is proposed by using a variable self-accelerating parameter. Firstly, a modified Newton method without memory with invariant parameter is constructed for solving nonlinear equations. Substituting the invariant parameter of
Xiaofeng Wang, Yuxi Tao
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