The construction of derivative-free iterative methods for approximating multiple roots a nonlinear equation is relatively new line research. This paper presents novel family one-parameter second-order techniques. Our schemes are free from derivatives and have been designed to find (m≥2). techniques involve the weight function approach. convergence analysis presented in main theorem. In addition...

Assays of specific activities and electrophoretic separations of multiple forms of 6-phosphogluconate dehydrogenase and peroxidase in cotton resistant and susceptible to Meloidogyne incognita were conducted 6 days after inoculation. Specific activities were greater in infected than in uninfected roots and also were greater in the resistant cultivar, 'Clevewilt 6-3-5,' than in the susceptible cu...

Finite mixtures of normal distributions are attractive in identifying the underlying group structure in the data. However, it is a challenging task to do statistical inference in normal mixture models using the method of maximum likelihood, due to the unbounded likelihood and the existence of multiple roots to the likelihood equation including a so-called spurious root. In this article we propo...

We present a symbolic-numeric technique to find the closest multivariate polynomial system to a given one which has roots with prescribed multiplicity structure. Our method generalizes the “Weierstrass iteration”, defined by Ruatta, to the case when the input system is not exact, i.e. when it is near to a system with multiple roots, but itself might not have multiple roots. First, using interpo...

in vitro multiple shoot regeneration of solanum nigrum l., an indian medicinal plant was accomplished on ms medium utilizing shoot tip and nodal explants. direct multiple shoots differentiated within 6 weeks when explants were cultured on ms medium containing bap (1.0-5.0 mg/l) and kin (1.0-5.0 mg/l) individually. among various concentrations of cytokinins tested, maximum number of multiple sho...

Given a degree n univariate polynomial f(x), the Budan-Fourier function Vf (x) counts the sign changes in the sequence of derivatives of f evaluated at x. The values at which this function jumps are called the virtual roots of f , these include the real roots of f and any multiple root of its derivatives. This concept was introduced (by an equivalent property) by Gonzales-Vega, Lombardi, Mahé i...

Given a multiple power sum (extending polynomial’s exponents to real numbers), the positive root isolation problem is to find a list of disjoint intervals, satisfying that they contain all positive roots and each of them contains exactly distinct one. In this paper, we develop the pseudo-derivative sequences for multiple power sums, then generalize Fourier’s theorem and Descartes’ sign rule for...

In this paper, we propose a new one-parameter family of Schröder’s method for finding the multiple roots of nonlinear equations numerically. Further, we derive many new cubically convergent families of Schröder-type methods. Proposed families are derived from the modified Newton’s method for multiple roots and one-parameter family of Schröder’s method. Furthermore, we introduce new families of ...

Cardinal’s matrix version of the Sebastiao e Silva polynomial root-finder rapidly approximates the roots as the eigenvalues of the associated Frobenius matrix. We preserve rapid convergence to the roots but amend the algorithm to allow input polynomials with multiple roots and root clusters. As in Cardinal’s algorithm, we repeatedly square the Frobenius matrix in nearly linear arithmetic time p...