43 citations · 58 across the 7 of their papers we have counts for
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A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich's and Dochev-Byrnev's methods
Petko D. Proinov
In this paper, we establish a general semilocal convergence theorem (with computationally verifiable initial conditions and error estimates) for iterative methods for simultaneous…
On a family of Weierstrass-type root-finding methods with accelerated convergence
Petko D. Proinov, Maria T. Vasileva
Kyurkchiev and Andreev (1985) constructed an infinite sequence of Weierstrass-type iterative methods for approximating all zeros of a polynomial simultaneously. The first member of…
On the convergence of high-order Ehrlich-type iterative methods for approximating all zeros of a polynomial simultaneously
Petko D. Proinov, Maria T. Vasileva
We study a family of high order Ehrlich-type methods for approximating all zeros of a polynomial simultaneously. Let us denote by the famous Ehrlich method (1967). Starti…
Relationships between different types of initial conditions for simultaneous root finding methods
Petko D. Proinov
The construction of initial conditions of an iterative method is one of the most important problems in solving nonlinear equations. In this paper, we obtain relationships between d…
General convergence theorems for iterative processes and applications to the Weierstrass root-finding method
Petko D. Proinov
In this paper, we prove some general convergence theorems for the Picard iteration in cone metric spaces over a solid vector space. As an application, we provide a detailed converg…
Semilocal convergence of two iterative methods for simultaneous computation of polynomial zeros
Petko D. Proinov
In this paper we study some iterative methods for simultaneous approximation of polynomial zeros. We give new semilocal convergence theorems with error bounds for Ehrlich's and Nou…