Cominimal Projections inln∞

Lipieta, Agnieszka

doi:10.1006/jath.1998.3221

Cited by 3 publications

(1 citation statement)

References 8 publications

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“…Proof. The proof is the consequence of theorem 1 by [Lipieta 1999] as well as theorem 3 by [Lipieta 2010]. Vector 0 q determining projection 0 Q has only one coordinate, namely 0 l , different from zero.…”

Section: Letmentioning

confidence: 89%

Existence and uniqueness of the producers’ optimal adjustment trajectory in a Debreu-type economy

Lipieta¹

2015

Mathematical Economics

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The aim of this paper is the analysis of adjustment processes in a Debreu-type economy. The reasons taken into account, e.g. incentives, cooperation of economic agents under full access to information, the way of sending messages described formally, are the basis for defining adjustment trajectories.Some reasons, such as introducing new legal requirements or implementing new profitable technologies formulated in mathematical language, can contribute to the transformation of the production sector and induce an appropriate way of adjusting the producers' plans of action.This survey relies on an examination of the relationships between quantities of goods and quantities of the productive factors used to produce them. As a result, the optimal producers' trajectories, due to the criterion of cost minimization, are defined. The paper also contains some remarks on the uniqueness of the trajectories under study.

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Section: Letmentioning

confidence: 89%

Existence and uniqueness of the producers’ optimal adjustment trajectory in a Debreu-type economy

Lipieta¹

2015

Mathematical Economics

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On the best conditioned bases of quadratic polynomials

Foucart

2004

Journal of Approximation Theory

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It is known that for P n , the subspace of C([−1, 1]) of all polynomials of degree at most n, the least basis condition number ∞ (P n ) (also called the Banach-Mazur distance between P n and n+1 ∞ ) is bounded from below by the projection constant of P n in C([−1, 1]). We show that ∞ (P n ) is in fact the generalized interpolating projection constant of P n in C([−1, 1]), and is consequently bounded from above by the interpolating projection constant of P n in C([−1, 1]). Hence the condition number of the Lagrange basis (say, at the Chebyshev extrema), which coincides with the norm of the corresponding interpolating projection and thus grows like O(ln n), is of optimal order, and for n = 2, 1.2201 . . . ∞ (P 2 ) 1.25.We prove that there is a basis u of P 2 such thatThis result means that no Lagrange basis of P 2 is best conditioned. It also seems likely that the previous value is actually the least basis condition number of P 2 , which therefore would not equal the projection constant of P 2 in C([−1, 1]). As for trigonometric polynomials of degree at most 1, we present numerical evidence that the Lagrange bases at equidistant points are best conditioned.

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The Optimal Producers’ Adjustment Trajectory

Lipieta

2015

Przegląd Statystyczny

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The trajectories illustrating the necessary changes in the production sphere, which are caused by the necessity or the wish of producers, who adjust their activities to the given requirements, are analyzed in the paper. The producers’ activities are modeled in the Debreu economy, while the requirements are given analytically, by using the linear functionals. If the producers change their plans of action due to the considered trajectories, equilibrium in the economy will be kept, although the initial state of equilibrium can be replaced by the other one. In the set of trajectories under study, the preference relation is defined. Under some assumptions, the maximal element of the above relation, so called the best producers’ adjustment trajectory, indicates the best path of changes in producers’ activities, under the criterion of losses minimization.

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Cominimal Projections inln∞

Cited by 3 publications

References 8 publications

Existence and uniqueness of the producers’ optimal adjustment trajectory in a Debreu-type economy

Existence and uniqueness of the producers’ optimal adjustment trajectory in a Debreu-type economy

On the best conditioned bases of quadratic polynomials

The Optimal Producers’ Adjustment Trajectory

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