Tatchi Ho

Publication Date


Document Type


Degree Name

M.S. (Master of Science)


Department of Mathematical Sciences


Riccati equation


This thesis is devoted to the study of the numerical methods for solving the continuous-time algebraic Riccati equation (CARE). In general, the numerical methods for the CARE can be divided in two major classes. The first class consists of methods that are based on the computation of the stable invariant subspace of the Hamiltonian matrix H. The methods in the second class approach the Riccati equation as a nonlinear algebraic equation through Newton iteration. There are many applications for the CARE. These equations arise in linear quadratic optimal-control problems and Kalman filtering problems, just to name two. We have selected eight numerical methods to describe, but we chose to compare seven methods. We have used a collection of 12 benchmark examples to compare the seven numerical methods for the CARE. Programs are written in MATLAB. The matrix sign function method has also been coded in Fortran 77 + LAPACK as well. MATLAB codes are provided in Appendix A. The codes for the CPU timing, flop counts, and Fortran 77 + LAPACK are provided in Appendix B. We have used different examples and matrix sizes to compare the accuracy of the seven algorithms. The absolute residuals, relative errors, and CPU times are reported as the results of the experiment. The results are provided in tables. A table of comparisons of different methods used in our experiment is presented at the end. It gives a guideline for practical uses of these methods based on this comparative study.


Includes bibliographical references (pages [64]-66)


v, 87 pages




Northern Illinois University

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