The inverse mean problem of geometric and contraharmonic means

被引：11
|
作者：
Lim, Y [1 ]
机构：
[1] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 408卷
基金：
新加坡国家研究基金会;
关键词：
geometric mean; contraharmonic mean; inverse mean problem; nonlinear matrix equation; positive definite matrix;
D O I：
10.1016/j.laa.2005.06.013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we solve the inverse mean problem of contraharmonic and geometric means of positive definite matrices (proposed in [W.N. Anderson, M.E. Mays, T.D. Morley, G.E. Trapp, The contraharmonic mean of HSD matrices, SIAM J. Algebra Disc. Meth. 8 (1987) 674-682]) [GRAPHICS] by proving its equivalence to the well-known nonlinear matrix equation X = T - BX-1B where T = 1/2(A + A#(A + 8BA(-1) B)) is the unique positive definite solution of X = A + 2BX(-1) B. The inverse mean problem is solvable if and only if B <= A. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：221 / 229
页数：9
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