An approximate solution of the Riccati matrix equation

Authors:
M. S. Henry and F. M. Stein

Journal:
Proc. Amer. Math. Soc. **25** (1970), 8-12

MSC:
Primary 34.04

DOI:
https://doi.org/10.1090/S0002-9939-1970-0261065-4

MathSciNet review:
0261065

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Riccati matrix equation has been the subject of several recent papers. In the present paper, the solution to this equation is approximated by a sequence of matrices whose elements are rational functions. It is shown that the sequence converges uniformly to the solution. Furthermore, each element of the sequence is constructed from a matrix polynomial which is in a sense the best approximation to the solution of the linear system associated with the Riccati matrix equation.

**[1]**Earl A. Coddington and Norman Levinson,*Theory of ordinary differential equations*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR**0069338****[2]**Philip J. Davis,*Interpolation and approximation*, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963. MR**0157156****[3]**Dunham Jackson,*The theory of approximation*, American Mathematical Society Colloquium Publications, vol. 11, American Mathematical Society, Providence, RI, 1994. Reprint of the 1930 original. MR**1451140****[4]**William T. Reid,*Riccati matrix differential equations and non-oscillation criteria for associated linear differential systems*, Pacific J. Math.**13**(1963), 665–685. MR**0155049****[5]**George F. Simmons,*Introduction to topology and modern analysis*, McGraw-Hill Book Co., Inc., New York-San Francisco, Calif.-Toronto-London, 1963. MR**0146625**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
34.04

Retrieve articles in all journals with MSC: 34.04

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1970-0261065-4

Keywords:
Riccati matrix equation,
associated Riccati system,
best approximation,
matrix polynomial,
bounded linear operation,
Banach algebra,
rational function,
rate of convergence

Article copyright:
© Copyright 1970
American Mathematical Society