Fast verified computation for solutions of algebraic Riccati equations arising in transport theory |
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| Authors: | Shinya Miyajima |
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| Institution: | Faculty of Science and Engineering, Iwate University, Iwate, Japan |
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| Abstract: | A fast algorithm for enclosing the solution of the nonsymmetric algebraic Riccati equation arising in transport theory is proposed. The equation has a special structure, which is taken into account to reduce the complexity. By exploiting the structure, the enclosing process involves only quadratic complexity under a reasonable assumption. The algorithm moreover verifies the uniqueness and minimal positiveness of the enclosed solution. Numerical results show the efficiency of the algorithm. |
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| Keywords: | nonsymmetric algebraic Riccati equation minimal positive solution verified computation M‐matrix Perron– Frobenius theory |
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