Related papers: Recursive families of higher order iterative maps
A novel family of integrable third order maps is presented. Each map possesses, by construction, a pair of rational invariants and a commuting map from the same class. The 3-dimensional invariant curve is parametrized, in general, by an…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
Root-finding method is an iterative process that constructs a sequence converging to a solution of an equation. Householder's method is a higher-order method that requires higher order derivatives of the reciprocal of a function and has…
Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\in\mathbb{F}^{N\times N}$ and a vector $b$, it is known that in the worst case $\Theta(N^2)$ operations over $\mathbb{F}$ are needed to…
A discrete map based on the sum of an integer's distinct primes factors and the sum of its other factors is defined and its iteration is studied.
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
Different variants of approximate inverse iteration like the locally optimal block preconditioned conjugate gradient method became in recent years increasingly popular for the solution of the large matrix eigenvalue problems arising from…
In this paper, we revisit the chaotic number of iterations needed by Newton's method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in…
In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.
In this paper, first we introduce a new mapping for finding a common fixed point of an infinite family of nonexpansive mappings then we consider iterative method for finding a common element of the set of fixed points of an infinite family…
This paper is devoted to proving an infinite sequence of relations for rooted tree maps. On the way, we also give a basis for the space of rooted tree maps.
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the present work, we define and study a new subclass of tree-like…
The enumeration of maps and the study of uniform random maps have been classical topics of combinatorics and statistical physics ever since the seminal work of Tutte in the sixties. Following the bijective approach initiated by Cori and…
An iterative square root of a function $f$ is a function $g$ such that $g(g(\cdot))=f(\cdot)$. We obtain new characterizations for detecting the non-existence of such square roots for self-maps on arbitrary sets. This is used to prove that…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
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…
New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences.…
We show that any graph polynomial from a wide class of graph polynomials yields a recurrence relation on an infinite class of families of graphs. The recurrence relations we obtain have coefficients which themselves satisfy linear…
We construct 9-parameter and 13-parameter dynamical systems of the plane which map bi-quadratic curves to other bi-quadratic curves and return to the original curve after two iterations. These generalize the QRT maps which map each such…