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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 | 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.

References [Enhancements On Off] (What's this?)

  • Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
  • Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963. MR 0157156
  • 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
  • William T. Reid, Riccati matrix differential equations and non-oscillation criteria for associated linear differential systems, Pacific J. Math. 13 (1963), 665–685. MR 155049
  • George F. Simmons, Introduction to topology and modern analysis, McGraw-Hill Book Co., Inc., New York-San Francisco, Calif.-Toronto-London, 1963. MR 0146625

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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