Results 1  10
of
179,029
of a Random Algebraic Polynomial
"... A random algebraic polynomial of degree $n $ is of the form $F_{n}(X, \omega)=k=0\sum a_{k(\omega}n)X^{k} $, where the $a_{k}(\omega) $ are random variables and $x $ is a complex number. Since Bloch and $\mathrm{P}\mathrm{o}\mathrm{l}\mathrm{y}\mathrm{a}[1]$ initiated the estimate of the number of r ..."
Abstract
 Add to MetaCart
A random algebraic polynomial of degree $n $ is of the form $F_{n}(X, \omega)=k=0\sum a_{k(\omega}n)X^{k} $, where the $a_{k}(\omega) $ are random variables and $x $ is a complex number. Since Bloch and $\mathrm{P}\mathrm{o}\mathrm{l}\mathrm{y}\mathrm{a}[1]$ initiated the estimate of the number
Abstract interpretation of algebraic polynomial systems (Extended Abstract)
 PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ALGEBRAIC METHODOLOGY AND SOFTWARE TECHNOLOGY, AMAST ’97
, 1997
"... We define a hierarchy of compositional formal semantics of algebraic polynomial systems over Falgebras by abstract interpretation. This generalizes classical formal language theoretical results and contextfree grammar flowanalysis algorithms in the same uniform framework of universal algebra and ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
We define a hierarchy of compositional formal semantics of algebraic polynomial systems over Falgebras by abstract interpretation. This generalizes classical formal language theoretical results and contextfree grammar flowanalysis algorithms in the same uniform framework of universal algebra
INEQUALITIES OF RAFALSON TYPE FOR ALGEBRAIC POLYNOMIALS
"... γn(dν; dµ): = sup π∈Pn\{0} π2 (x)dν(x) − ∞ π2 (x)dµ(x), can be represented by the zeros of orthogonal polynomials corresponding to dµ in case (i) dν(x) = (A + Bx)dµ(x), where A + Bx is nonnegative on the support of dµ and (ii) dν(x) = (A + Bx 2)dµ(x), where dµ is symmetric and A + Bx 2 is nonnegat ..."
Abstract
 Add to MetaCart
γn(dν; dµ): = sup π∈Pn\{0} π2 (x)dν(x) − ∞ π2 (x)dµ(x), can be represented by the zeros of orthogonal polynomials corresponding to dµ in case (i) dν(x) = (A + Bx)dµ(x), where A + Bx is nonnegative on the support of dµ and (ii) dν(x) = (A + Bx 2)dµ(x), where dµ is symmetric and A + Bx 2
AN EXTREMUM PROBLEM CONCERNING ALGEBRAIC POLYNOMIALS
, 1986
"... Let S „ he the set of all polynomials whose degree does not exceed n and whose all zeros are real but lie outside ( 1, 1). Similarly, we say p"E Q „ if p,(x) is a real polynomial whose all zeros lie outside the open disk with center at the origin and radius l. Further we will denote by H „ the ..."
Abstract
 Add to MetaCart
Let S „ he the set of all polynomials whose degree does not exceed n and whose all zeros are real but lie outside ( 1, 1). Similarly, we say p"E Q „ if p,(x) is a real polynomial whose all zeros lie outside the open disk with center at the origin and radius l. Further we will denote by H
Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree
 J. Fourier Anal. Appl
, 1995
"... For any fixed " ? 0 we construct an orthonormal Schauder basis fp g 1 =0 for C[\Gamma1; 1] consisting of algebraic polynomials p with deg p (1 + "). The orthogonality is with respect to the Chebyshev weight. AMS classification: 41 A 05, 41 A 10, 65 D 05 Key words and phrases: Schau ..."
Abstract

Cited by 10 (6 self)
 Add to MetaCart
For any fixed " ? 0 we construct an orthonormal Schauder basis fp g 1 =0 for C[\Gamma1; 1] consisting of algebraic polynomials p with deg p (1 + "). The orthogonality is with respect to the Chebyshev weight. AMS classification: 41 A 05, 41 A 10, 65 D 05 Key words and phrases
Uniform and Pointwise Shape Preserving Approximation by Algebraic Polynomials
, 2011
"... We survey developments, over the last thirty years, in the theory of Shape Preserving Approximation (SPA) by algebraic polynomials on a finite interval. In this article, “shape ” refers to (finitely many changes of) monotonicity, convexity, or qmonotonicity of a function. It is rather well known th ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We survey developments, over the last thirty years, in the theory of Shape Preserving Approximation (SPA) by algebraic polynomials on a finite interval. In this article, “shape ” refers to (finitely many changes of) monotonicity, convexity, or qmonotonicity of a function. It is rather well known
ON REPRESENTATIONS OF ALGEBRAIC POLYNOMIALS BY SUPERPOSITIONS OF PLANE WAVES
, 1942
"... Abstract. Let P be a bivariate algebraic polynomial of degree n with the real senior part, and Y = {yj}n1 an nelement collection of pairwise noncolinear unit vectors on the real plane. It is proved that there exists a rigid rotation Y ϕ of Y by an angle ϕ = ϕ(P, Y) ∈ [0, pi/n] such that P equals ..."
Abstract
 Add to MetaCart
Abstract. Let P be a bivariate algebraic polynomial of degree n with the real senior part, and Y = {yj}n1 an nelement collection of pairwise noncolinear unit vectors on the real plane. It is proved that there exists a rigid rotation Y ϕ of Y by an angle ϕ = ϕ(P, Y) ∈ [0, pi/n] such that P
EXPECTED DISCREPANCY FOR ZEROS OF RANDOM ALGEBRAIC POLYNOMIALS
"... Abstract. We study asymptotic clustering of zeros of random polynomials, and show that the expected discrepancy of roots of a polynomial of degree n, with not necessarily independent coefficients, decays like √ log n/n. Our proofs rely on discrepancy results for deterministic polynomials, and order ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. We study asymptotic clustering of zeros of random polynomials, and show that the expected discrepancy of roots of a polynomial of degree n, with not necessarily independent coefficients, decays like √ log n/n. Our proofs rely on discrepancy results for deterministic polynomials, and order
On Different Classes of Algebraic Polynomials with Random Coefficients
, 2008
"... The expected number of real zeros of the polynomial of the form a0 � a1x � a2x2 � ·· · � anxn, where a0,a1,a2,...,an is a sequence of standard Gaussian random variables, is known. For n large it is shown that this expected number in �−∞, ∞ � is asymptotic to �2/π � log n. In this paper, we show tha ..."
Abstract
 Add to MetaCart
The expected number of real zeros of the polynomial of the form a0 � a1x � a2x2 � ·· · � anxn, where a0,a1,a2,...,an is a sequence of standard Gaussian random variables, is known. For n large it is shown that this expected number in �−∞, ∞ � is asymptotic to �2/π � log n. In this paper, we show
AN ANALOG METHOD FOR THE ROOT SOLUTION OF ALGEBRAIC POLYNOMIALS
, 1958
"... Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the aut ..."
Abstract
 Add to MetaCart
Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Results 1  10
of
179,029