Certain Generalized q-Operators by Prakash Om, Sharma Diwaker, Maheshwari Prerna

“…The applications of q-calculus in the approximation theory is a very interesting area of research in the recent years, several new q-operators were introduced and their behaviour were discussed by many researchers. …”
Get full text

On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals by G.A. Yessenbayeva, A.N. Yesbayev, N.K. Syzdykova, M.A. Smirnova

“… The article is devoted to research on approximation theory. When approximating functions by trigonometric polynomials, the spectrum is chosen from various sets. …”
Get full text

Vibration Analysis of Rotating Functionally Graded Cylindrical Shells with Orthogonal Stiffeners by Tran Minh Tu, Nguyen Van Loi

“…Based on Love's first approximation theory and smeared stiffeners technique, the governing equations of motion which take into account the effects of initial hoop tension and also the centrifugal and Coriolis forces due to rotation are derived. …”
Get full text

Robust Adaptive Modified Newton Algorithm for Generalized Eigendecomposition and Its Application by Yanmin Sheng, Wei Guo, Hong-Sheng Xi, Feng Yang, Jian Yang

“…A rigorous analysis of its convergence properties is presented by using stochastic approximation theory. We also apply this theory to solve the signal reception problem of multicarrier DS-CDMA to illustrate its practical application. …”
Get full text

Existence of Time-Scale Class of Three Dimensional Fractional Differential Equations by Rabha W. Ibrahim, Maslina Darus

“…This technique is very useful in approximation theory.</p>…”
Get full text

Existence of Time-Scale Class of Three Dimensional Fractional Differential Equations by Rabha W. Ibrahim, Maslina Darus

“…This technique is very useful in approximation theory.</p>…”
Get full text

أثر بعض التحويلات المحافظة على منحنيات ريس وعلى معامل الاستمرار by محمد علي

“…In this paper we study the effect of some conformal mappings (linear , inversion and Joukowski) on two terms from approximation theory of complex functions. We find that these functions  transform the curves from Riesz class  into curves from the same class. …”
Get full text

A certain sequence of functions involving the Aleph function by Agarwal P., Chand M., Onur Kiymaz İ., Çetinkaya A.

“…Sequences of functions play an important role in approximation theory. In this paper, we aim to establish a (presumably new) sequence of functions involving the Aleph function by using operational techniques. …”
Get full text

Unveiling the Potential of Sheffer Polynomials: Exploring Approximation Features with Jakimovski–Leviatan Operators by Mohra Zayed, Shahid Ahmad Wani, Mohammad Younus Bhat

“…The application of approximation theory has earned significant attention from scholars globally, particularly in the fields of engineering and mathematics. …”
Get full text

Describing phase transitions in field theory by self-similar approximants by Yukalov V.I., Yukalova E.P.

“…Self-similar approximation theory is shown to be a powerful tool for describing phase transitions in quantum field theory. …”
Get full text

Quasi-Herglotz functions and convex optimization by Y. Ivanenko, M. Nedic, M. Gustafsson, B. L. G. Jonsson, A. Luger, S. Nordebo

“…In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.…”
Get full text

أثر بعض التحويلات المحافظة على منحنيات ريس وعلى معامل الاستمرار by محمد علي

“…In this paper we study the effect of some conformal mappings (linear , inversion and Joukowski) on two terms from approximation theory of complex functions. We find that these functions  transform the curves from Riesz class  into curves from the same class. …”
Get full text

An Overview of Some Issues in the Theory of Deep Networks by Poggio, Tomaso, Banburski, Andrzej

“…We review our contributions in the areas of approximation theory and optimization. We also introduce a new approach based on cross-validation leave-one-out stability to estimate bounds on the expected error of overparametrized classifiers, such as deep networks. © 2020 Institute of Electrical Engineers of Japan. …”
Get full text

Networks and the Best Approximation Property by Girosi, Federico, Poggio, Tomaso

“…From the point of view of approximation theory, however, the property of approximating continous functions arbitrarily well is not sufficient for characterizing good approximation schemes. …”
Get full text

On the Convergence of Stochastic Iterative Dynamic Programming Algorithms by Jaakkola, Tommi, Jordan, Michael I., Singh, Satinder P.

“…In this paper we provide a rigorous proof of convergence of these DP-based learning algorithms by relating them to the powerful techniques of stochastic approximation theory via a new convergence theorem. The theorem establishes a general class of convergent algorithms to which both TD(lambda) and Q-learning belong.…”
Get full text

A THEOREM IN FINE POTENTIAL-THEORY AND APPLICATIONS TO FINELY HOLOMORPHIC-FUNCTIONS by Lyons, T

“…We use the Hartog theorem, rational approximation theory, and results proved in a previous paper by the author to prove that the derivative of a finely holomorphic function exists everywhere and is finely holomorphic. © 1980.…”

How smooth is quantum complexity? by Bulchandani, VB, Sondhi, S

“…We use ideas from Diophantine approximation theory and sub-Riemannian geometry to rigorously quantify this lack of smoothness. …”

AN INTERPOLATION THEORY APPROACH TO H-INFINITY CONTROLLER DEGREE-BOUNDS by Limebeer, D, Anderson, B

“…This paper, which uses interpolation theory, complements a previous paper which addresses the same problem through an approach based on approximation theory. We demonstrate that the interpolation theory approach is more direct and circumvents a number of the technical difficulties in the previous method: the final outcome is a much shorter proof. …”

An extension of MATLAB to continuous functions and operators by Battels, Z, Trefethen, L

“…Applications in approximation theory and numerical analysis are explored, and possible extensions for more substantial problems of scientific computing are mentioned.…”

Approximating the pth root by composite rational functions by Gawlik, ES, Nakatsukasa, Y

“…A landmark result from rational approximation theory states that x 1/p on [0, 1] can be approximated by a type-(n, n) rational function with root-exponential accuracy. …”