Related papers: General convergence theorems for iterative process…
We present a geometric proof of the averaging theorem for perturbed dynamical systems on a Riemannian manifold, in the case where the flow of the unperturbed vector field is periodic and the $\mathbb{S}^{1}$-action associated to this vector…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
We estabish an analog of the Cauchy-Poincare separation theorem for normal matrices in terms of majorization. Moreover, we present a solution to the inverse spectral problem (Borg-type result) for a normal matrix. Using this result we…
Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
In this paper we analyse the Waveholtz method, a time-domain iterative method for solving the Helmholtz iteration, in the constant-coefficient case in all of $\mathbb{R}^d$. We show that the difference between a Waveholtz iterate and the…
We extend the well-known Rainwater-Simons convergence theorem to various generalized convergence methods such as strong matrix summability, statistical convergence and almost convergence. In fact we prove these theorems not only for…
The computation of generalized inverses of quaternion matrices is a fundamental problem in quaternion linear algebra, with wide-ranging applications in signal processing, image restoration, and multidimensional data analysis. This paper…
This paper proposes an efficient algorithm for testing copositivity of homogeneous polynomials over the positive semidefinite cone. The algorithm is based on a novel matrix optimization reformulation and requires solving a hierarchy of…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation of the method allows an analysis in a complex variables…
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…
The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised…
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some…
Newton's method for polynomial root finding is one of mathematics' most well-known algorithms. The method also has its shortcomings: it is undefined at critical points, it could exhibit chaotic behavior and is only guaranteed to converge…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
We prove the universality theorem for the iterated integrals of logarithms of $L$-functions in the Selberg class on some line parallel to the real axis.
Following a systematic analysis of existing results, we investigate when complete interlacing between the zeros of distinct polynomial sequences, $\{\mathcal{P}_n\}$ and $\{\mathcal{G}_n\}$ can be achieved by using a naturally arising extra…
While numerous extensions of Banach's fixed point theorem typically offer only sufficient conditions for the existence and uniqueness of a fixed point and the convergence of iterative sequences, this study introduces a generalization…