相关论文: On two families of iterative methods without memor…
In this study, several interesting iterative sequences were investigated. First, we define the iterative sequences. We fix function f(n). An iterative sequence starts with a natural number n, and calculates the sequence f(n),f(f(n)),…
The classical division algorithm for polynomials requires $O(n^2)$ operations for inputs of size $n$. Using reversal technique and Newton iteration, it can be improved to $O({M}(n))$, where ${M}$ is a multiplication time. But the method…
This work wishes to support various mathematical issues concerning the iterative methods with the help of new programming languages. We consider a way to show how problems in math have an answer by using different academic resources and…
In this article, we introduce two families of novel fractional $\theta$-methods by constructing some new generating functions to discretize the Riemann-Liouville fractional calculus operator $\mathit{I}^{\alpha}$ with a second order…
The evolution equations mentioned in the title of this paper read as follows: x~n = P(n)(x1; x2) , n = 1, 2 , where l is the "discrete-time" independent variable taking integer values (l =0, 1, 2, ...), xn = xn (l) are the 2 dependent…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
We introduce a new class of optimal iterative methods without memory for approximating a simple root of a given nonlinear equation. The proposed class uses four function evaluations and one first derivative evaluation per iteration and it…
We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with…
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering…
On a domain of the n-dimensional Euclidean space, and for an integer k=1,...,n, the k-Hessian equations are fully nonlinear elliptic equations for k >1 and consist of the Poisson equation for k=1 and the Monge-Ampere equation for k=n. We…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
The classification of natural exponential families started with the paper \cite {Morri} where Carl Morris unifies six very familiar families by the fact that their variance functions are polynomials of degree less or equal to two. Extension…
We study the factorization of the numbers $N = X^2+c$, where $c$ is a fixed constant, and this independently of the value of gcd$(X,c)$. We prove the existence of a family of sequences with arithmetic difference $(U_n, Z_n)$ generating…
Natural Gradient Descent, a second-degree optimization method motivated by the information geometry, makes use of the Fisher Information Matrix instead of the Hessian which is typically used. However, in many cases, the Fisher Information…
In a series of papers \cite{LSJR16, PP17, LPP}, it was established that some of the most commonly used first order methods almost surely (under random initializations) and with step-size being small enough, avoid strict saddle points, as…
We introduce a family of proximal discontinuous Galerkin methods for variational inequalities, focusing on the obstacle problem as a didactic example. Each member of this family is born from applying a different well-known nonconforming…
We consider the following equations: \begin{equation*} \left\{\begin{array}{ll} (-\triangle)^{\alpha/2}u(x)=f(v(x)), \\ (-\triangle)^{\beta/2}v(x)=g(u(x)), &x \in R^{n},\\ u,v\geq 0, &x \in R^{n}, \end{array} \right. \end{equation*} for…
We review a family of algorithms for Lyapunov- and Riccati-type equations which are all related to each other by the idea of \emph{doubling}: they construct the iterate $Q_k = X_{2^k}$ of another naturally-arising fixed-point iteration…
New families of composition methods with processing of order 4 and 6 are presented and analyzed. They are specifically designed to be used for the numerical integration of differential equations whose vector field is separated into three or…
Through introducing a new iterative formula for divided differnce using Neville's and Aitken's algorithms,we study new iterative methods for interpolation,numerical differentiation and numerical integration formulas with arbitrary order of…