Related papers: Lidstone Fractal Interpolation and Error Analysis
In this work, we introduce the new class of functions which can use to solve the nonlinear/linear multi-dimensional differential equations. Based on these functions, a numerical method is provided which is called the Developed Lagrange…
We present the Fast Newton Transform (FNT), an algorithm for performing $m$-variate Newton interpolation in downward closed polynomial spaces with time complexity $\mathcal{O}(|A|m\overline{n})$. Here, $A$ is a downward closed set of…
We revisit the notion of nuclear parton-to-pion fragmentation functions at next-to-leading order accuracy as an effective description of hadroproduction in nuclear environments such as in semi-inclusive lepton-nucleus deep-inelastic…
Federated Learning (FL) is a novel approach that allows for collaborative machine learning while preserving data privacy by leveraging models trained on decentralized devices. However, FL faces challenges due to non-uniformly distributed…
Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one…
The relation between nonanticipative Rate Distortion Function (RDF) and filtering theory is discussed on abstract spaces. The relation is established by imposing a realizability constraint on the reconstruction conditional distribution of…
High-precision interpolation of LISA phase measurements allows signal reconstruction and formulation of Time-Delay Interferometry (TDI) combinations to be conducted in post-processing. The reconstruction is based on phase measurements made…
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…
In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function $f$ defined on the interval $[a,b]$, this formula is derived by introducing a linear combination of $f'$ computed at $n+1$…
This paper presents an efficient method to compute the maximum likelihood (ML) estimation of the parameters of a complex 2-D sinusoidal, with the complexity order of the FFT. The method is based on an accurate barycentric formula for…
Classical Laguerre spectral approximations are highly effective on the half-line when the target function is smooth in the usual polynomial scale. However, their accuracy deteriorates for nonsmooth functions. Such behavior appears naturally…
It's well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It's of the form$% | f(x)-s(x)| \leq (Cd)^{\frac{c}{d}}\left\Vert f\right\Vert_{h}$ where $C,c$ are constants, $h$ is the…
An effective approach for construction of simple approximation for description of non-ideality effects in classical one- and two-component plasma model is under discussion. General constraints i.e. positiveness and exponential type for…
This paper uses the Continued Fraction Expansion (CFE) method for analog realization of fractional order differ-integrator and few special classes of fractional order (FO) controllers viz. Fractional Order Proportional-Integral-Derivative…
In this paper, based on Newton interpolation we have proposed a numerical scheme of predictor-corrector type in order to solve fractional differential equations with the fractional derivative involving the Mittag-Leffler function. We have…
Long-time-integrated quantities in stochastic processes, in or out of equilibrium, usually exhibit rare but huge fluctuations. Work or heat production is such a quantity, of which the probability distribution function displays an…
In this paper, we analyze the accuracy of gradient estimates obtained by linear interpolation when the underlying function is subject to bounded measurement noise. The total gradient error is decomposed into a deterministic component…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
Several groups have recently investigated the flow of information in high-energy collisions, from the entanglement entropy of the proton yielding classical Shannon entropy of its parton distribution functions (pdfs), through jet splitting…
Fractal Interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant…