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Iterated Integrals and Borwein–Chen–Dilcher Polynomials
We study the zero location and the asymptotic behavior of iterated integrals of polynomials. Borwein–Chen–Dilcher’s polynomials play an important...
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Testing Polynomials for Vanishing on Cartesian Products of Planar Point Sets: Collinearity Testing and Related Problems
We present subquadratic algorithms, in the algebraic decision-tree model of computation, for detecting whether there exists a triple of points,...
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Annulus containing all the eigenvalues of a matrix polynomial
In this paper, we prove a more general result concerning the location of the eigenvalues of a matrix polynomial in an annulus from which we deduce an...
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Extremal problems of Turán-type for a univariate complex coefficient polynomial
In this paper, we establish some new inequalities in the plane that are inspired by some classical Turán-type inequalities that relate the norm of a...
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Egerváry's theorems for harmonic trinomials
We study the arrangements of the roots in the complex plane for the lacunary harmonic polynomials called harmonic trinomials. We provide necessary...
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Computation of Optimal Linear Strong Stability Preserving Methods Via Adaptive Spectral Transformations of Poisson–Charlier Measures
Strong stability preserving (SSP) coefficients govern the maximally allowable step-size at which positivity or contractivity preservation of...
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A note on Perron’s irreducibility criterion
In this note, we generalize the classical irreducibility criterion of Perron and obtain numerous other new irreducibility criteria for polynomials...
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Continued Fractions, Hurwitz and Stieltjes
In the chapter on Signal Processing we found out that the stability of filters or difference equations is equivalent to the fact that certain...
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Darboux Transformations for Orthogonal Polynomials on the Real Line and on the Unit Circle
Jacobi matrices constitute a communicating vessel between orthogonal polynomials on the real line (OPRL) and the theory of self-adjoint operators. In...
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Numerical Solution of the Cauchy Problem Based on the Basic Element Method
AbstractA fundamentally new approach to the numerical solution of the Cauchy problem for ODEs based on polynomials in the form of basic elements is...
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Cauchy–de Branges Spaces, Geometry of Their Reproducing Kernels and Multiplication Operators
Cauchy–de Branges spaces are Hilbert spaces of entire functions defined in terms of Cauchy transforms of discrete measures on the plane and...
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Characterizations of the Maximum Likelihood Estimator of the Cauchy Distribution
AbstractThis paper gives a new approach for the maximum likelihood estimation of the joint of the location and scale of the Cauchy distribution. We...
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From Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear Functionals
In this contribution, we present an overview of standard orthogonal polynomials by using an algebraic approach. Discrete Darboux transformations of...
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On Sendov’s Conjecture
Sendov’s Conjecture asserts that if all the zeros of a polynomial p lie inside the closed unit disk then a closed unit disk centered at each of its...
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Identification of the Domain, Ranges, and Values of Complex Roots of a Polynomial with Complex Coefficients Based on Stable Address Sorting
In this paper, we present a method of programmatic identification of complex roots of polynomials with complex coefficients without specifying the...
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Gegenbauer and Other Planar Orthogonal Polynomials on an Ellipse in the Complex Plane
We show that several families of classical orthogonal polynomials on the real line are also orthogonal on the interior of an ellipse in the complex...
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Search of Complex Transcendental Roots of a Combination of a Nonlinear Equation and a Polynomial
Target nonlinear equation is limited within ordinary differential equations with one-point boundary value or two-point boundary value problems, and...