发表机构
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València（瓦伦西亚理工大学多学科数学大学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一类基于Heun方法引入权函数的四阶矩阵迭代族，并给出五阶特例，通过动力学分析确定稳定成员，数值实验验证了其性能。
AI 中文摘要
在作者的研究领域中，开发高效的迭代格式以逼近逆矩阵和广义逆矩阵具有重要意义。为此，通过将适当的权函数引入标量Heun方法，建立了一族用于逼近逆矩阵和广义逆矩阵的四阶矩阵迭代格式。此外，作为所提出族的一个特定成员，还获得了一种五阶矩阵迭代格式。在适当条件下，确定了所提出族的理论收敛阶，并通过动力学分析识别出其稳定成员。为了评估其性能并验证理论结果的一致性，对不同规模的矩阵进行了数值测试。
英文摘要
The development of efficient iterative schemes for approximating the inverse and generalized inverse matrices is important in my research fields. To this end, a family of fourth-order matrix iterative schemes for approximating the inverse and generalized inverse matrices is established by incorporating an appropriate weight function into the scalar Heun method. Moreover, a fifth-order matrix iterative scheme is obtained as a particular member of the proposed family. Under suitable conditions, the theoretical order of convergence is determined for the proposed family, whose stable members are identified through dynamical analysis. To assess their performance and verify the consistency of the theoretical results, some numerical tests are performed on matrices of different sizes.
