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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: 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?)

  • [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
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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