On polynomials with positive coefficients

Erdélyi, Tamás; Szabados, J.

doi:10.1016/0021-9045(88)90119-0

Cited by 20 publications

(30 citation statements)

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“…Other interesting bounds for the Lorentz degree of constrained polynomials and some applications to Markov and Bernstein type inequalities for derivatives can be found in [4,6]. Generalization of Lorentz degree to trigonometric polynomials has been studied in [7].…”

Section: Degree Elevation Of Bézier Curves and Lorentz Degreementioning

confidence: 98%

On the Lorentz degree of a product of polynomials

Ait‐Haddou

2015

Journal of Approximation Theory

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Section: Degree Elevation Of Bézier Curves and Lorentz Degreementioning

confidence: 98%

On the Lorentz degree of a product of polynomials

Ait‐Haddou

2015

Journal of Approximation Theory

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“…Choosing m = n makes the representation unique but also imposes a restriction on the location of the complex zeroes of q n (x) [9]. The smallest number m for which the positive polynomial q n (x) can be written in the form (5) is called the Lorentz degree of q n (x).…”

Section: The Lorentz Representationmentioning

confidence: 99%

Comonotone and coconvex rational interpolation and approximation

2011

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Comonotonicity and coconvexity are well-understood in uniform polynomial approximation and in piecewise interpolation. The covariance of a global (Hermite) rational interpolant under certain transformations, such as taking the reciprocal, is well-known, but its comonotonicity and its coconvexity are much less studied. In this paper we show how the barycentric weights in global rational (interval) interpolation can be chosen so as to guarantee the absence of unwanted poles and at the same time deliver comonotone and/or coconvex interpolants. In addition the rational (interval) interpolant is wellsuited to reflect asymptotic behaviour or the like.

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“…The representation, (7), of a polynomial, with s k unrestricted in sign, is referred to as a Lorentz representation of a polynomial by Milovanović, Mitrinović and Rassias (1994). Erdelyi and Szabados (1988) refer to polynomials, which have a representation (7) with all s k non-negative or all s k non-positive, as Lorentz polynomials. Cargo and Shisha (1966) state and prove Lemma 1, and call it (rightly) the Bernstein form of a polynomial.…”

Section: Related Literaturementioning

confidence: 99%

Ranking investment projects

Foster¹,

Mitra²

2003

Economic Theory

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This paper describes conditions under which one investment project dominates a second project in terms of net present value, irrespective of the choice of the discount rate. The resulting partial ordering of projects has certain similarities to stochastic dominance. However, the structure of the net present value function leads to characterizations that are quite specific to this context. Our theorems use Bernstein's (1915) innovative results on the representation and approximation of polynomials, as well as other general results from the theory of equations, to characterize the partial ordering. We also show how the ranking is altered when the range of discount rates is limited or the rate varies period by period. Copyright Springer-Verlag Berlin Heidelberg 2003JEL Classification Numbers: D92, G31, H043, O22., Keywords and Phrases: Investment projects, Present value, Stochastic dominance, Polynomials, Rate of return over cost, Time dominance.,

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On polynomials with positive coefficients

Cited by 20 publications

References 2 publications

On the Lorentz degree of a product of polynomials

On the Lorentz degree of a product of polynomials

Comonotone and coconvex rational interpolation and approximation

Ranking investment projects

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