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* Supported by the Army Research Office under grant DAAD-19-02-10059.Bounds on the error of certain penalized least squares data fitting methods are derived. In addition to general results in a fairly abstract setting, more detailed results are included for several particularly interesting special cases, including splines in both one and several variables.

Permanence de relations de récurrence dans certains développements asymptotiques. (Permanence of recurrence relations in certain asymptotic expansions).

Robin, Guy (1988)

Publications de l'Institut Mathématique. Nouvelle Série

Perturbations of an Ostrowski type inequality and applications.

Ujević, Nenad (2002)

International Journal of Mathematics and Mathematical Sciences

Perturbations of Best Approximation Problems.

Philip M. Anselone, Joel Davis (1973)

Numerische Mathematik

Piecewise approximation and neural networks

Martina Révayová, Csaba Török (2007)

Kybernetika

The paper deals with the recently proposed autotracking piecewise cubic approximation (APCA) based on the discrete projective transformation, and neural networks (NN). The suggested new approach facilitates the analysis of data with complex dependence and relatively small errors. We introduce a new representation of polynomials that can provide different local approximation models. We demonstrate how APCA can be applied to especially noisy data thanks to NN and local estimations. On the other hand,...

Piecewise atone interpolation of monotone operators

Eduardo H. Zarantonello (1982)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Piecewise L-Splines.

P.M. Prenter (1971/1972)

Numerische Mathematik

Piecewise Polynomial Spaces and Geometric Continuity of Curves.

Charles A. Micchelli, Nira Dyn (1989)

Numerische Mathematik

Point derivations and prime ideals in R(X)

Joel Feinstein (1991)

Studia Mathematica

Points minimaux dans les espaces de Banach

B. Beauzamy (1974/1975)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Points minimaux dans les espaces de Banach (suite)

B. Beauzamy (1974/1975)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Pointwise approximation by Meyer-König and Zeller operators

Xiao-Ming Zeng, Jun-Ning Zhao (2000)

Annales Polonici Mathematici

We study the rate of pointwise convergence of Meyer-König and Zeller operators for bounded functions, and get an asymptotically optimal estimate.

Pointwise convergence for expansions in surface harmonics of arbitrary dimension.

E.L. Roetman (1976)

Journal für die reine und angewandte Mathematik

Pointwise estimates for modified positive linear operators

Cao, Jia-Ding, Gonska, Heinz H. (1989)

Portugaliae mathematica

Pointwise inequalities and approximation in fractional Sobolev spaces

David Swanson (2002)

Studia Mathematica

We prove that a function belonging to a fractional Sobolev space $L^{α, p} (ℝ ⁿ)$ may be approximated in capacity and norm by smooth functions belonging to $C^{m, λ} (ℝ ⁿ)$ , 0 < m + λ < α. Our results generalize and extend those of [12], [4], [14], and [11].

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