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

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Abstract

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.

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Acknowledgements

The author would like to thank the reviewers for their valuable comments.

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  1. Faculty of Science and Engineering, Iwate University, 4-3-5 Ueda, Morioka-shi, Iwate, 020-8551, Japan

    Shinya Miyajima

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  1. Shinya Miyajima
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Correspondence to Shinya Miyajima.

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This work was supported in part by JSPS KAKENHI Grant Numbers JP16K05270, JP21K03363.

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Miyajima, S. Fast enclosure for the minimal nonnegative solution to the nonsymmetric T-Riccati equation. Calcolo 59, 31 (2022). https://doi.org/10.1007/s10092-022-00475-4

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  • DOI: https://doi.org/10.1007/s10092-022-00475-4

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