Estimations of Karcher mean by Hadamard product

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-09-27 DOI:10.1016/j.laa.2024.09.013

Masatoshi Fujii , Yuki Seo , Masaru Tominaga

引用次数: 0

Abstract

In this paper, we estimate the difference between the Hadamard product and the Karcher mean of n positive invertible operators on the Hilbert space in terms of the Specht ratio and the Kantorovich constant. Also, we improve the obtained inequalities in the case of

n = 2

. Moreover, we give ratio inequalities of the operator power means by the Hadamard product.

查看原文本刊更多论文

用 Hadamard 乘积估算 Karcher 平均值

在本文中，我们用 Specht 比值和 Kantorovich 常量来估计希尔伯特空间上 n 个正可逆算子的 Hadamard 乘积和 Karcher 平均值之间的差异。同时，我们改进了 n=2 情况下的不等式。此外，我们还给出了哈达玛积的算子幂级数的比率不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.