Related papers: New Iterative Methods for Interpolation, Numerical…
Iterative algorithms for differential privacy run for a fixed number of iterations, where each iteration learns some information from data and produces an intermediate output. However, the algorithm only releases the output of the last…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
Results about existence and uniqueness of solutions of initial value problem for certain types of partial differential equations are recalled as well as iterative scheme and an error estimate for approximate solutions obtained using this…
In this article, we discuss sixth-order and seventh-order iterative methods for nonlinear equations. Derivative-based and derivative-free, both categories are presented for said iterative methods. Especially sixth-order derivative-based and…
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free…
The aim of this paper is to analyse the gain of the update algorithm associated to the recently proposed D-iteration: the D-iteration is a fluid diffusion based new iterative method. It exploits a simple intuitive decomposition of the…
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
This paper presents a methodology for constructing iterative schemes of any order of convergence for solving nonlinear systems of equations. It also provides formulas for the order of convergence of any iterative schemes constructed using…
Iterative imputation is a popular tool to accommodate missing data. While it is widely accepted that valid inferences can be obtained with this technique, these inferences all rely on algorithmic convergence. There is no consensus on how to…
A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
In this paper, we consider a discrete version of iterated integrals by the naive (equally divided) Riemann sum. In particular, basic three formulas for usual iterated integrals are discritized. Moreover, we proved cyclic sum formulas for…
We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained…
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…
We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…
In this paper, to begin with, we review six different analytical methods which are widely used to derive symmetries, integrating factors, multipliers, Darboux polynomials and integrals of second order nonlinear ordinary differential…