Related papers: On root-ratio multipoint methods for finding multi…
In this paper we investigate iterative roots of strictly monotone upper semi-continuous multifunctions having finitely many jumps. Known results are concerning roots of order 2 for multifunctions of exact one jump. For the general…
In this study, we consider an optimization problem with uncertainty dependent on decision variables, which has recently attracted attention due to its importance in machine learning and pricing applications. In this problem, the gradient of…
This article provides a simple trigonometric method for determining how many roots of a quartic equation are real and how many are complex, without solving the equation. The approach replaces the quartic's classical discriminant -- a…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
Among many existing algorithms, convergence methods are the most popular means of computing square root and the reciprocal of square root of numbers. An initial approximation is required in these methods. Look up tables (LUT) are employed…
Linearized polynomials appear in many different contexts, such as rank metric codes, cryptography and linear sets, and the main issue regards the characterization of the number of roots from their coefficients. Results of this type have…
We made a comparative analysis of numerical methods for multidimensional optimization. The main parameter is a number of computations of the test function to reach necessary accuracy, as it is computationally "slow". For complex functions,…
We are concerned with the tensor equation with an M-tensor or Z-tensor, which we call the M- tensor equation or Z-tensor equation respectively. We derive a necessary and sufficient condition for a Z (or M)-tensor equation to have…
Algorithms for computing rational generating functions of solutions of one-dimensional difference equations are well-known and easy to implement. We propose an algorithm for computing rational generating functions of solutions of…
We obtained the formulas for the quantities of positive, negative and zero values of the Mobius function for any real x in terms of the Mobius function values for square root of x - similar to the identities we found earlier for the Mertens…
Some difficulties regarding the application of the well-known sieve method are considered in the case when a practical (program) realization of selecting elements, having a particular property among the elements of a set with a sufficiently…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
We address univariate root isolation when the polynomial's coefficients are in a multiple field extension. We consider a polynomial $F \in L[Y]$, where $L$ is a multiple algebraic extension of $\mathbb{Q}$. We provide aggregate bounds for…
In this paper methods for simultaneous finding all roots of generalized polynomials are developed. These methods are related to the case when the roots are multiple. They possess cubic rate of convergence and they are as labour-consuming as…
This paper revisits an algorithm for isolating real roots of univariate polynomials based on continued fractions. It follows the work of Vincent, Uspen- sky, Collins and Akritas, Johnson and Krandick. We use some tricks, especially a new…
We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms.…
We present a continuation method to compute all zeros of a harmonic mapping $f$ in the complex plane. Our method works without any prior knowledge of the number of zeros or their approximate location. We start by computing all solution of…
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…
Given a polynomial system f associated with a simple multiple zero x of multiplicity {\mu}, we give a computable lower bound on the minimal distance between the simple multiple zero x and other zeros of f. If x is only given with limited…
Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms for factoring such polynomials and related tasks (such as…