In this paper, we are concerned with the problem of counting the multiplicities of a zero-dimensional regular set’s zeros. We generalize the squarefree decomposition of univariate polynomials to the so-called pseudo squarefree decomposition of multivariate polynomials, and then propose an algorithm for decomposing a regular set into a finite number of simple sets. From the output of this algori...

If one considers a sampled-data system derived from a continuous-time system with a relative degree of one or two on a finite-time interval, it is not simple to predict the behavior of the output of the inverse of the sampled-data system as the sampling period goes to zero. This is because the number of sample points increases while the zeros of the pulse-transfer function tend to the boundary ...

The topological degree of a continuous mapping is implemented for the calculation of the total number of the simple real zeros within any interval of the Bessel functions of first and second kind and their derivatives. A new algorithm, based on this implementation, is given for the localization and isolation of these zeros. Furthermore, a second algorithm is presented for their computation empl...

Discrete-time linear periodic single-input/single-output (SISO) systems having uniform relative degree are considered. A closed-form expression of the blocking input is derived and exploited to obtain a computationally advantageous characterization of the structural zeros. Indeed, it suffices to compute the eigenvalues of a suitably defined (n • n) matrix, where n is the system order. It is sho...

Bounds for the distance |cν,s− cν±1,s′ | between adjacent zeros of cylinder functions are given; s and s′ are such that @cν,s′′ ∈ ]cν,s, cν±1,s′ [; cν,k stands for the kth positive zero of the cylinder (Bessel) function Cν(x) = cosαJν(x)− sinαYν(x), α ∈ [0, π[, ν ∈ R. These bounds, together with the application of modified (global) Newton methods based on the monotonic functions fν(x) = x2ν−1Cν...

‎Let $p(z)$ be a polynomial of degree $n$ and for a complex number $alpha$‎, ‎let $D_{alpha}p(z)=np(z)+(alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $alpha$‎. ‎Dewan et al proved‎ ‎that if $p(z)$ has all its zeros in $|z| leq k, (kleq‎ ‎1),$ with $s$-fold zeros at the origin then for every‎ ‎$alphainmathbb{C}$ with $|alpha|geq k$‎, ‎begin{align*}‎ ‎max_{|z|=...

Carstensen, C. and M.S. PetkoviC, On iteration methods without derivatives for the simultaneous determination of polynomial zeros, Journal of Computational and Applied Mathematics 45 (1993) 251-266. Several algorithms for simultaneously approximating simple complex zeros of a polynomial are presented. These algorithms use Weierstrass’ corrections and do not require any polynomial derivatives. I...

The purpose of the present paper is to examine zeros R-Bonacci polynomials and their derivatives. We obtain new characterizations for these polynomials. Our results generalize ones obtained special case r=2. Furthermore, we find explicit formulas roots derivatives in some cases. are substantially simple useful.

We consider sums of the form $\sum \phi(\gamma)$, where $\phi$ is a given function, and $\gamma$ ranges over ordinates nontrivial zeros Riemann zeta-function in interval. show how numerical estimation such can be accelerated by simple device, give examples involving both convergent divergent infinite sums.

Due to higher-order Kaup-Newell (KN) system has more complex and diverse solutions than classical second-order flow KN system, the research on it attracted attention. In this paper, we consider a equation with third order dispersion quintic nonlinearity. Based theory of inverse scattering, matrix Riemann-Hilbert problem is established. Through dressing method, solution simple zeros without refl...