An approximate solution of the Riccati matrix equation
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- by M. S. Henry and F. M. Stein
- Proc. Amer. Math. Soc. 25 (1970), 8-12
- DOI: https://doi.org/10.1090/S0002-9939-1970-0261065-4
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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
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- 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
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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