A note on algebraic Riccati equations associated with reducible singular M-matrices

TL;DR

This paper proves a conjecture about solutions to algebraic Riccati equations linked to reducible singular M-matrices, improving understanding of algorithms used to compute these solutions.

Contribution

It establishes a proof for a conjecture concerning minimal nonnegative solutions of algebraic Riccati equations related to reducible singular M-matrices.

Findings

Proves a conjecture about minimal nonnegative solutions.

Enhances understanding of doubling algorithms.

Provides theoretical insights into algebraic Riccati equations.

Abstract

We prove a conjecture about the minimal nonnegative solutions of algebraic Riccati equations associated with reducible singular M-matrices. The result enhances our understanding of the behaviour of doubling algorithms for finding the minimal nonnegative solutions.