Studies on quadratic matrix equations and riccati differential equations associated with regular m-matrices

The thesis is mainly about the quadratic matrix equation X2- EX- F = 0, where E is a diagonal matrix and F is a regular M-matrix. Quadratic matrix equations of this kind arise in noisy Wiener-Hopf problems for Markov chains. The solution of practical interest is a special M-matrix solution. The existence and uniqueness of M-matrix solutions and some numerical methods for nding the required M-matrix solution are studied by transforming the equation into a nonsymmetric algebraic Riccati equation for which the four coe cient matrices form a regular M-matrix. We also discuss the initial value problem for a matrix Riccati di erential equation associated with a regular M-matrix. We show that for suitable initial matrices X0, the initial value problem has a global solution X(t) on [0;1): Moreover, we show that X(t) converges, as t ! 1, to the stable equilibrium solution, which is the minimal nonnegative solution of corresponding algebraic Riccati equation.

Name thesis:degree_name

Master of Science (MSc)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

Faculty of Graduate Studies and Research, University of Regina

Year dc:date.issued

2017

Author dc:creator

• Roy, Anupam

Advisor dc:contributor.advisor

• Guo, Chun-Hua

Committee member dc:contributor.committeemember

• Floricel, Remus

Language dc:language.iso

en

DOI

https://doi.org/10.82465/4178

OAI identifier oai:identifier

oai:uregina.scholaris.ca:10294/7713