Operator-valued Semicircular Elements: Solving A Quadratic Matrix Equation with Positivity Constraints

被引：55

作者：

Helton, J. William ^{[2
]}

Far, Reza Rashidi ^{[1
]}

Speicher, Roland ^{[1
]}

机构：

[1] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada

[2] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2007年 / 2007卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

D O I：

10.1093/imrn/rnm086

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the quadratic matrix equation VW + eta(W) W = I, for given V with positive real part and given analytic mapping. with some positivity preserving properties, has exactly one solution W with positive real part. Also we provide and compare numerical algorithms based on the iteration underlying our proofs. This work bears on operator-valued free probability theory, in particular on the determination of the asymptotic eigenvalue distribution of band or block random matrices.

引用

页数：15

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