Volume 40, pp. 489-506, 2013.

Vector extrapolation applied to algebraic Riccati equations arising in transport theory

Rola El-Moallem and Hassane Sadok


We apply the reduced rank extrapolation method (RRE) to an iterative method for computing the minimal positive solution of a nonsymmetric algebraic Riccati equation that arises in transport theory. The computations yield the minimal positive solution of a vector equation, which is derived from the special form of solutions of the Riccati equation and by exploiting the special structure of the coefficient matrices of the Riccati equation. Numerical experiments and comparisons illustrate the effectiveness of the new approach.

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Key words

nonsymmetric algebraic Riccati equation, transport theory, minimal positive solution, iterative methods, vector sequences, polynomial vector extrapolation methods, convergence acceleration, reduced rank extrapolation.

AMS subject classifications

15A24, 65F10, 65B05

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