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

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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]**E. A. Coddington and N. Levinson,*Theory of ordinary differential equations*, McGraw-Hill, New York, 1965. MR**0069338 (16:1022b)****[2]**P. J. Davis,*Interpolation and approximation*, Blaisdell, Waltham, Mass., 1963. MR**28**#393. MR**0157156 (28:393)****[3]**D. Jackson,*The theory of approximation*, Amer. Math. Soc. Colloq. Publ., vol. XI, Amer. Math. Soc., Providence, R. I., 1930. MR**1451140 (98a:01022)****[4]**W. T. Reid,*Riccati matrix differential equations and non-oscillation criteria for associated linear differential systems*, Pacific J. Math.**13**(1963), 665-685. MR**27**#4991. MR**0155049 (27:4991)****[5]**G. F. Simmons,*Introduction to topology and modern analysis*, McGraw-Hill, New York, 1963. MR**26**#4145. MR**0146625 (26:4145)**

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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