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.
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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