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Approximation methods for a class of discrete Wiener-Hopf equations

Nowak M. A.

Opuscula Mathematica

2009

Vol. 29, no. 3

271-288

In this paper, we consider approximation methods for operator equations of the form Au + Bu = ƒ, where A is a discrete Wiener-Hopf operator on lp (1≤ p < ∞) which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on perturbation B and ƒ are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.

Approximation properties of some two-layer feedforward neural networks

Nowak M. A.

Opuscula Mathematica

2007

Vol. 27, no. 1

59-72

In this article, we present a multiyariate two-layer feedforward neural networks that approximate continuos functions defined on [0, 1]d. We show that the L1 error of approximation is asymptotically proportional to the modulus of continuity of the underlying function taken at √d/n, where n is the number of function values used.

Ekonofizyka [rec.]

Nowak M. A.

Postępy Fizyki

2005

T. 56, z. 6

279-280

Recenzja książki: Rosario N. Mantegna, H. Eugene Stanley - Ekonofizyka: Wprowadzenie, przekład Ryszard Kutner, Wydawnictwo Naukowe PWN, Warszawa 2001, s. 164.