涉及加权几何平均的若干矩阵方程及其应用研究

Kalpa Publications in Engineering Pub Date : 1900-01-01 DOI:10.29007/7sj7

Xuân Đại Lê, Tuan Pham, Thi Hong Linh Nguyen, N. Tran, V. Dang

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引用次数: 0

摘要

本文考虑了两个涉及加权几何平均的矩阵方程。利用正定矩阵锥上的不动点定理证明了正定解的唯一存在性。此外，我们还研究了这些方程的多步平稳迭代方法，并证明了相应的收敛性。作为矩阵方程的一种应用，介绍了基于矩阵几何均值的量子态保真度度量方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Study On Some Matrix Equations Involving The Weighted Geometric Mean and Their Application

In this paper we consider two matrix equations that involve the weighted geometric mean. We use the fixed point theorem in the cone of positive definite matrices to prove the existence of a unique positive definite solution. In addition, we study the multi-step stationary iterative method for those equations and prove the corresponding convergence. A fidelity measure for quantum states based on the matrix geometric mean is introduced as an application of matrix equation.

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