相关论文: Fixed-point analysis of Ogita-Aishima's symmetric …

Optimization problems with access to only zeroth-order information of the objective function on Riemannian manifolds arise in various applications, spanning from statistical learning to robot learning. While various zeroth-order algorithms…

We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by L\'opez-Acedo and Xu to find common fixed points of finite families of $k$-strict pseudocontractive…

This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…

In this paper, the existence and uniqueness of the fixed point for the product of two nonlinear operator in Banach algebra is discussed. In addition, an approximation method of the fixed point of hybrid nonlinear equations in Banach…

The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well established since many decades. This topic was mostly studied for variational formulations…

The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…

A thorough backward stability analysis of Hotelling's deflation, an explicit external deflation procedure through low-rank updates for computing many eigenpairs of a symmetric matrix, is presented. Computable upper bounds of the loss of the…

We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…

A local and parallel algorithm based on the multilevel discretization is proposed in this paper to solve the eigenvalue problem by the finite element method. With this new scheme, solving the eigenvalue problem in the finest grid is…

The initial value problem for a multivalued differential equation is studied, which is governed by the sum of a monotone, hemicontinuous, coercive operator fulfilling a certain growth condition and a Volterra integral operator in time of…

The balance between convergence and diversity is a key issue of evolutionary multi-objective optimization. The recently proposed stable matching-based selection provides a new perspective to handle this balance under the framework of…

In this paper we establish new renormalized oscillation theorems for discrete symplectic eigenvalue problems with Dirichlet boundary conditions. These theorems present the number of finite eigenvalues of the problem in arbitrary interval…

In this paper, we discuss numerical methods for the eigenvalue decomposition of real symmetric matrices. While many existing methods can compute approximate eigenpairs with sufficiently small backward errors, the magnitude of the resulting…

We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the…

In the present paper, we study a multipoint boundary value problem for a system of Fredholm integro-differenial equations by the method of parameterization. The case of a degenerate kernel is studied separately, for which we obtain…

We prove an Obata-type rigidity result for the spherical cap and apply it for an eigenvalue problem with mixed boundary condition.

Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…

It is significant and challenging to solve eigenvalue problems of partial differential operators when many highly accurate eigenpair approximations are required. The adaptive finite element discretization based parallel orbital-updating…

In this paper, we establish some new fixed point theorems and coincidence point theorems for essential distances and $e^{0}$-metrics which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point…