Low-rank approximation to the solution of a nonsymmetric algebraic Riccati equation from transport theory

Weng, Peter Chang Yi; Fan, Hung Yuan; Chu, Eric King-wah

doi:10.1016/j.amc.2012.06.066

Cited by 8 publications

(2 citation statements)

References 25 publications

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“…In recent years, efficient numerical algorithms for finding the minimal positive solution of Equation have been extensively studied (e.g., see previous studies). On the other hand, these algorithms rely on floating point arithmetic, so that rounding errors are included in the obtained result.…”

Section: Introductionmentioning

confidence: 99%

“…Here • is the Hadamard product, T = (T ij ) = (1∕( i + d j )), and u and v satisfy the vector equations In recent years, efficient numerical algorithms for finding the minimal positive solution of Equation 1 have been extensively studied (e.g., see previous studies 2,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] ). On the other hand, these algorithms rely on floating point arithmetic, so that rounding errors are included in the obtained result.…”

Section: Introductionmentioning

confidence: 99%

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Fast verified computation for solutions of algebraic Riccati equations arising in transport theory

Miyajima

2017

Numerical Linear Algebra App

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Summary 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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Section: Introductionmentioning

confidence: 99%