CONTINUED FRACTION EXPANSIONS OF REAL POWERS OF POSITIVE DEFINITE MATRICES WITH APPLICATIONS TO MATRIX MEANS

M. Raiessoulli; A. Kacha; S. Salhi

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CONTINUED FRACTION EXPANSIONS OF REAL POWERS OF POSITIVE DEFINITE MATRICES WITH APPLICATIONS TO MATRIX MEANS

机译：正定矩阵有功的连续分数展开式及其在矩阵均值中的应用

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摘要

The aim of this paper is to provide some results and applications for continued fractions with matrix arguments. First, we introduce a continued fraction expansion of A~α where A is a positive definite matrix and α a positive real. Then we provide an application to matrix means (defined below), which makes their computation practical as well as efficient. At the end, some numerical examples are discussed.

机译：本文的目的是为带有矩阵参数的连续分数提供一些结果和应用。首先，我们引入A〜α的连续分数展开式，其中A为正定矩阵，α为正实数。然后，我们为矩阵均值（定义如下）提供了一个应用程序，使它们的计算既实用又高效。最后，讨论了一些数值示例。

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来源
《Arabian Journal for Science and Engineering. Section A, Sciences》 |2006年第1a期|p.41-55|共15页
作者
M. Raiessoulli; A. Kacha; S. Salhi;
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作者单位

Department of Mathematics, Faculty of Sciences Meknes, Morocco;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类自然科学总论;
关键词
positive definite matrix; continued fraction expansion with matrices arguments; convergence; geometric matrix means;

机译：正定矩阵;带有矩阵参数的连续分数展开;收敛;几何矩阵均值;

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1. CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES [J] . Ali Kacha Algebras, groups and geometries . 2007,第3期

机译：正定矩阵的某些函数的连续分数展开式
2. EXPANSION OF WEIGHTED PSEUDOINVERSE MATRICES WITH POSITIVE DEFINITE WEIGHTS INTO MATRIX POWER PRODUCTS. ITERATIVE METHODS [J] . I. V. Sergienko, E. F. Galba, V. S. Deineka Cybernetics and Systems Analysis . 2007,第1期

机译：将正定权重的加权拟逆矩阵扩展为矩阵乘积。迭代方法
3. The riemannian geometry of the space of positive-definite matrices and its application to the regularization of positive-definite matrix-valued data [J] . Moakher M., Zéra? M. Journal of mathematical imaging and vision . 2011,第2期

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4. Szasz's Inequalitices for Meta-Positive Definite Matrices and Similar Generalized Positive Definite Matrices [C] . Yanxi Li The Third International Workshop on Applied Matrix Theory（第三届国际矩阵分析与应用会议）论文集 . 2009

机译：亚正定矩阵和类似广义正定矩阵的Szasz不等式
5. High-quality preconditioning techniques for multi-length-scale symmetric positive definite matrices and their applications to the hybrid quantum Monte Carlo simulation of the Hubbard model. [D] . Yamazaki, Ichitaro. 2008

机译：多长度尺度对称正定矩阵的高质量预处理技术及其在哈伯德模型的混合量子蒙特卡罗模拟中的应用。
6. Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging [O] . Hongtu Zhu, Yasheng Chen, Joseph G. Ibrahim, -1

机译：正定矩阵的本征回归模型在扩散张量成像中的应用
7. Powers of matrices with positive definite real part [O] . Charles R. Johnson 1975

机译：矩阵的力量与正定的真实部位
8. Minimal Realizations of Transfer-Function Matrices by Means of Matrix Continued Fraction. [R] . Shieh, L. S., Wei, Y. J., Yates, R. 1975

机译：基于矩阵连续分数的传递函数矩阵的最小实现。

CONTINUED FRACTION EXPANSIONS OF REAL POWERS OF POSITIVE DEFINITE MATRICES WITH APPLICATIONS TO MATRIX MEANS

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