Analysis and Numerical Methods for Algebraic Riccati Equations Associated with Regular M-Matrices
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.
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Faculty of Graduate Studies and Research, University of Regina