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Fast verified computation for solutions of algebraic Riccati equations arising in transport theory
Authors:Shinya Miyajima
Affiliation:Faculty of Science and Engineering, Iwate University, Iwate, Japan
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.
Keywords:nonsymmetric algebraic Riccati equation  minimal positive solution  verified computation  M‐matrix  Perron–  Frobenius theory
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