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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
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.

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