相关论文: Iterative roots of exclusive multifunctions
Some easily verifiable sufficient conditions for the nonexistence of iterative roots for multifunctions on arbitrary nonempty sets are presented. Typically if the graph of the multifunction has a distinguished point with a relatively large…
In the present study, we propose necessary and sufficient assumptions on the coefficients in order to only get distinct real roots of polynomials.
We give closed form expressions for the numbers of multi-rooted plane trees with specified degrees of root vertices. This results in an infinite number of integer sequences some of which are known to have an alternative interpretation. We…
In this paper a special type of difference equations is investigated. The impulses start abruptly at some points and their action continue on given finite intervals. This type of equations is used to model a real process. An algorithm,…
In this paper, we present monotone sequences of lower and upper bounds on the Perron value of a nonngeative matrix, and we study their strict monotonicity. Using those sequences, we provide two combinatorial applications. One is to improve…
Many problems in applied mathematics require root finding algorithms. Unfortunately, root finding methods have limitations. Firstly, regarding the convergence, there is a trade-off between the size of it's domain and it's rate. Secondly the…
We devise a simple but remarkably accurate iterative routine for calculating the roots of a polynomial of any degree. We demonstrate that our results have significant improvement in accuracy over those obtained by methods used in popular…
Recursive maps of high order of convergence $m$ (say $m=2^{10}$ or $m=2^{20}$) induce certain monotone step functions from which one can filter relevant information needed to globally separate and compute the real roots of a function on a…
We use the method of monotone iterations to obtain fixed point and coupled fixed point results for mixed monotone operators in the setting of partially ordered sets, with no additional assumptions on the partial order and with no…
We obtain new upper bounds on the number of distinct roots of lacunary polynomials over finite fields. Our focus will be on polynomials for which there is a large gap between consecutive exponents in the monomial expansion.
We present sufficient conditions, in terms of the jumping kernels, for two large classes of conservative Markov processes of pure-jump type to be purely discontinuous martingales with finite second moment. As an application, we establish…
We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with…
In this paper, we give some counting results on integer polynomials of fixed degree and bounded height whose distinct non-zero roots are multiplicatively dependent. These include sharp lower bounds, upper bounds and asymptotic formulas for…
We describe a method for calculating the roots of special functions satisfying second order linear ordinary differential equations. It exploits the recent observation that the solutions of a large class of such equations can be represented…
Iteration methods based on barycentric rational interpolation are derived that exhibit accelerating orders of convergence. For univariate root search, the derivative-free methods approach quadratic convergence and the first-derivative…
We present a new algorithm for refining a real interval containing a single real root: the new method combines characteristics of the classical Bisection algorithm and Newton's Iteration. Our method exhibits quadratic convergence when…
We establish a sufficient condition for the ultimate positivity of P-recursive sequences of arbitrary order with a unique dominant root. By additionally verifying finitely many initial terms, the positivity can also be resolved. As an…
Mixed trigonometric-polynomials (MTPs) are functions of the form $f(x,\sin{x}, \cos{x})$ with $f\in\mathbb{Q}[x_1,x_2,x_3]$. In this paper, an algorithm ``isolating" all the real roots of an MTP is provided and implemented. It automatically…
We introduce the notion of `core growth rate' for strongly synchronizing transducers. We explore some elementary properties of the core growth rate and give examples of transducers with exponential core growth rate. We conjecture that all…
Highly efficient and even nearly optimal algorithms have been developed for the classical problem of univariate polynomial root-finding (see, e.g., \cite{P95}, \cite{P02}, \cite{MNP13}, and the bibliography therein), but this is still an…