On Approximate Bounds of Zeros of Polynomials within and on the Unit Disc
نویسنده
چکیده
Current interest of researchers is to study the location of zero of polynomials as such they have been writing extensively on the works based on Gauss [4] and Cauchy [2]. Numerous books and papers have been written in modern areas of digital signal processing, Communication theory, Control theory and Cryptography, to mention a few and since then there is a greater need for improving the bounds of the zeros of the polynomials. In this paper we show that if all the coefficient of class of polynomials are numerically less than unity. Then our method gives the sharper bounds as compared to the ones given by Affane-Aji et al [1]. Moreover, we show by way of examples that their estimated bounds over estimate our bounds in all the cases under present investigation.
منابع مشابه
Solving singular integral equations by using orthogonal polynomials
In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...
متن کاملComputing sharp and scalable bounds on errors in approximate zeros of univariate polynomials
There are several numerical methods for computing approximate zeros of a given univariate polynomial. In this paper, we develop a simple and novel method for determining sharp upper bounds on errors in approximate zeros of a given polynomial using Rouche's theorem from complex analysis. We compute the error bounds using non-linear optimization. Our bounds are scalable in the sense that we compu...
متن کاملSome compact generalization of inequalities for polynomials with prescribed zeros
Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$. In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$, $k^2 leq rRleq R^2$ and for $Rleq r leq k$. Our results refine and generalize certain well-known polynomial inequalities.
متن کاملUsing Chebyshev polynomial’s zeros as point grid for numerical solution of nonlinear PDEs by differential quadrature- based radial basis functions
Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are...
متن کامل