Related papers: Approximate Solutions of Functional Equations
The error term in the approximate functional equation for exponential sums involving the divisor function will be improved under certain conditions for the parameters of the approximate functional equation.
We introduce a method of approximate nonclassical Lie-B\"acklund symmetries for partial differential equations with a small parameter and discuss applications of this method to finding of approximate solutions both integrable and…
Derivative-matching approximations are constructed as power series built from functions. The method assumes the knowledge of special values of the Bell polynomials of the second kind, for which we refer to the literature. The presented…
The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…
In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out very easily calculating for the analytic Fourier-Feynman transform of…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
In this short note, we propose an unified method to derive formulas for derivations conjugated by exponential functions on an almost complex manifold. In v3, we corrected some mistakes in previous versions.
This paper presents a novel systematic methodology to obtain new simple and tight approximations, lower bounds, and upper bounds for the Gaussian Q-function, and functions thereof, in the form of a weighted sum of exponential functions.…
We study the optimization of functions with $n>2$ arguments that have a representation as a sum of several functions that have only $2$ of the $n$ arguments each, termed sums of bivariates, on finite domains. The complexity of optimizing…
In this paper we consider the numerical solution of Fractional Differential Equations by means of $m$-step recursions. The construction of such formulas can be obtained in many ways. Here we study a technique based on the rational…
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…
We obtain matching direct and inverse theorems for the degree of weighted $L_p$-approximation by polynomials with the Jacobi weights $(1-x)^\alpha (1+x)^\beta$. Combined, the estimates yield a constructive characterization of various…
We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: first, we prove that…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
Surrogate assisted evolutionary algorithms (EA) are rapidly gaining popularity where applications of EA in complex real world problem domains are concerned. Although EAs are powerful global optimizers, finding optimal solution to complex…
In the underlying study it is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear and multivalued functional differential equations like: \begin{eqnarray*} u^\prime(t) &\in&…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…