Related papers: Approximation of fuzzy numbers by convolution meth…
Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were…
Diffusion models have become the go-to method for many generative tasks, particularly for image-to-image generation tasks such as super-resolution and inpainting. Current diffusion-based methods do not provide statistical guarantees…
This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…
The power of fuzz testing lies in its random, often brute-force, generation and execution of inputs to trigger unexpected behaviors and vulnerabilities in software applications. However, given the reality of infinite possible input…
We present new convolution based smooth approximations to the absolute value function and apply them to construct gradient based algorithms such as the nonlinear conjugate gradient scheme to obtain sparse, regularized solutions of linear…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…
We calculate the least upper bounds of pointwise and uniform approximations for classes of $2\pi$-periodic functions expressible as convolutions of an arbitrary square summable kernel with functions, which belong to the unit ball of the…
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
Being exact at both short- and long-time limits, the Gaussian approximation is widely used to calculate neutron incoherent inelastic scattering functions in liquids. However, to overcome a few numerical difficulties, extra physical…
A general method for estimating the approximation numbers of composition operators on $\Ht$, using finite-dimensional model subspaces, is studied and applied in the case when the symbol of the operator maps the unit disc to a domain whose…
This paper shows a novel fuzzy approximate reasoning method based on the least common multiple (LCM). Its fundamental idea is to obtain a new fuzzy reasoning result by the extended distance measure based on LCM between the antecedent fuzzy…
The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
One possible data encryption scheme is related to stream ciphers, which use a sufficiently long pseudo-random sequence. To increase the cryptographic strength of the cipher, linear shift algorithms (generated by linear recurrent sequences…
Given the first 20-100 coefficients of a typical generating function of the type that arises in many problems of statistical mechanics or enumerative combinatorics, we show that the method of differential approximants performs surprisingly…
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with $\alpha$-H\"older derivatives (for some $0<\alpha\leq 1$). The smooth approximation is given by means of an…
In some applications, one is interested in reconstructing a function $f$ from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we…
The approximation properties of the finite element method can often be substantially improved by choosing smooth high-order basis functions. It is extremely difficult to devise such basis functions for partitions consisting of arbitrarily…
In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated through a small set of smooth functions. The invariance is either by translations under a…
We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) `admissible'…