Analysis and Numerical Methods for Algebraic Riccati Equations Associated with Regular M-Matrices
type: CreativeWork
description: The thesis is a further study about algebraic Riccati equations for which the four coe cient matrices form a regular M-matrix K. We prove a property about minimal nonnegative solutions of such an algebraic Riccati equation and its dual equation. And we show that Newton's method, SDA, ADDA are well-de ned and quadratically convergent in non-critical case. Then we prove that ADDA is linearly convergent with rate 1=2 in critical case. As compared to earlier work on solving regular MARE by ADDA, the results we present here are more general. This thesis extends the knowledge of doubling algorithms.
abstract: The thesis is a further study about algebraic Riccati equations for which the four coe cient matrices form a regular M-matrix K. We prove a property about minimal nonnegative solutions of such an algebraic Riccati equation and its dual equation. And we show that Newton's method, SDA, ADDA are well-de ned and quadratically convergent in non-critical case. Then we prove that ADDA is linearly convergent with rate 1=2 in critical case. As compared to earlier work on solving regular MARE by ADDA, the results we present here are more general. This thesis extends the knowledge of doubling algorithms.
author: Lu, Di
language: en
date published: 2015-12
date modified: 2026-07-24T04:03:49Z
provider: University of Regina
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Faculty of Graduate Studies and Research, University of Regina

PropertyValue
property ID: Handle
value: https://hdl.handle.net/10294/6862

PropertyValue
property ID: DOI
value: 10.82465/4990