Fast enclosure for the minimal nonnegative solution to the nonsymmetric T-Riccati equation

A fast algorithm is proposed for numerically computing 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 solution contained in the in...

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Bibliographic Details
Published inCalcolo Vol. 59; no. 3
Main Author Miyajima, Shinya
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2022
Springer Nature B.V
Subjects
Algorithms
Mathematics
Mathematics and Statistics
Numerical Analysis
Riccati equation
Theory of Computation
15A24
65G20
Verified numerical computation
65F30
Minimal nonnegative solution
matrix
T-Riccati equation
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Summary:A fast algorithm is proposed for numerically computing 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 solution contained in the interval matrix is unique and equal to the minimal nonnegative solution. Numerical results show the efficiency of the algorithm.
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-022-00475-4