We propose a fast numerical algorithm which computes an interval matrix containing the minimal nonnegative solution to the nonsymmetric T-Riccati equation. The cost of this algorithm is cubic plus that for numerically solving the equation. The algorithm proves that the minimal nonnegative solution exists, the Kronecker form of the associated Fréchet derivative at the solution is an M-matrix, and the solution contained in the interval matrix is unique and the minimal nonnegative solution. Numerical results illustrate efficiency of the algorithm.
REFERENCES
1.
P.
Benner
and D.
Palitta
, “On the solution of the nonsymmetric T-Riccati equation
”, Electron. Trans. Numer. Anal.
54
, 68
–88
(2021
).2.
S.
Miyajima
, “Fast verified computation for solutions of continuous-time algebraic Riccati equations
”, Jpn. J. Ind. Appl. Math.
32
, 529
–544
(2015
).3.
S. M.
Rump
, “INTLAB - INTerval LABoratory”, in Developments in Reliable Computing
, edited by T.
Csendes
(Kluwer Academic Publishers
, Dordrecht
, 1999
), pp. 77
–104
.
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