Related papers: Lidstone Fractal Interpolation and Error Analysis
The relation between rate distortion function (RDF) and Bayesian filtering theory is discussed. The relation is established by imposing a causal or realizability constraint on the reconstruction conditional distribution of the RDF, leading…
The two-parameter Mittag-Leffler function $E_{\alpha, \beta}$ is of fundamental importance in fractional calculus. It appears frequently in the solutions of fractional differential and integral equations. Nonetheless, this vital function is…
In this article, we have employed fractal formalism to calculate the Fracture Functions of the Leading neutron produced in \textit{ep} collisions. The fractal concept describes the self-similar behavior of the proton structure at Leading…
We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric…
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…
The main purpose of this note is to show that in a realization $(x_{1}^{n}, y_{1}^{n})$ of the causal \textit{information rate-distortion function} (IRDF) for a $\kappa$-th order Markovian source $x_{1}^{n}$, under a single letter sum…
The primary objectives of this paper are to present the construction of bivariate fractal interpolation functions over triangular interpolating domain using the concept of vertex coloring and to propose a double integration formula for the…
The feedback particle filter (FPF) is an innovative, control-oriented and resampling-free adaptation of the traditional particle filter (PF). In the FPF, individual particles are regulated via a feedback gain, and the corresponding gain…
We show that highly accurate approximations can often be obtained from constructing Thiele interpolating continued fractions by a Greedy selection of the interpolation points together with an early termination condition. The obtained…
The main result of this paper states that for a given countable system of data, there exists a countable iterated function system consisting of Rakotch contractions, such that its attractor is the graph of a fractal interpolation function…
In this paper we study a family of limsup sets that are defined using iterated function systems. Our main result is an analogue of Khintchine's theorem for these sets. We then apply this result to the topic of intrinsic Diophantine…
Given $ -\infty< \lambda < \Lambda < \infty $, $ E \subset \mathbb{R}^n $ finite, and $ f : E \to [\lambda,\Lambda] $, how can we extend $ f $ to a $ C^m(\mathbb{R}^n) $ function $ F $ such that $ \lambda\leq F \leq \Lambda $ and $…
This paper introduces a "kernel-independent" interpolative decomposition butterfly factorization (IDBF) as a data-sparse approximation for matrices that satisfy a complementary low-rank property. The IDBF can be constructed in $O(N\log N)$…
We recently introduced an efficient methodology to perform density-corrected Hartree-Fock density functional theory (DC(HF)-DFT) calculations and an extension to it we called "corrected" HF DFT (C(HF)-DFT). In this work, we take a further…
We establish several new fractal and number theoretical phenomena connected with expansions which are generated by infinite linear iterated function systems. First of all we show that the systems $\Phi$ of cylinders of generalized L\"uroth…
In the first part of this paper, we define a deep convolutional neural network connected with the fractional Fourier transform (FrFT) using the $\theta$-translation operator, the translation operator associated with the FrFT. Subsequently,…
A powerful statistical interpolating concept, which we call \emph{fully lifted} (fl), is introduced and presented while establishing a connection between bilinearly indexed random processes and their corresponding fully decoupled (linearly…
Predictions of observable properties by density-functional theory calculations (DFT) are used increasingly often in experimental condensed-matter physics and materials engineering as data. These predictions are used to analyze recent…
The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this…
The interpolation-regression approximation is a powerful tool in numerical analysis for reconstructing functions defined on square or triangular domains from their evaluations at a regular set of nodes. The importance of this technique lies…