Computing sharp and scalable bounds on errors in approximate zeros of univariate polynomials

On Bounds For The Zeros of Univariate Polynomials

Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated. Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds fo...

On Bounds For The Zeros of Univariate Polynomial

Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated. Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds fo...

On the average number of sharp crossings of certain Gaussian random polynomials

On the Location of Zeros of Complex Polynomials

This paper proves bounds for the zeros of complex valued polynomials. The assertions stated in this work have been specialized in the area of the location of zeros for complex polynomials in terms of two foci: (i) finding bounds for complex valued polynomials with special conditions for the coefficients and (ii) locating zeros of complex valued polynomials without special conditions for the coe...

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...