A modified structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equations from transport theory

Guo, Pei-Chang; Guo, Xin

doi:10.1016/j.cam.2013.09.058

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…Available iteration algorithms are the Newton's method [4-6, 10, 16, 20], the fixed-point iteration method [1,2,8,14,15] and the structure-preserving doubling algorithm [3,7,9,11,17,19].…”

Section: Introductionmentioning

confidence: 99%

A modified large-scale structure-preserving doubling algorithm for a large-scale Riccati equation from transport theory

Guo

2015

Numer Algor

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A large scale nonsymmetric algebraic Riccati equation XCX−XE−AX+ B = 0 arising in transport theory is considered, where the n × n coefficient matrices B, C are symmetric and low-ranked and A, E are rank one updates of nonsingular diagonal matrices. By introducing a balancing strategy and setting appropriate initial matrices carefully, we can simplify the large-scale structure-preserving doubling algorithm (SDA ls) for this special equation. We give modified large-scale structurepreserving doubling algorithm, which can reduce the flop count of original SDA ls by half. Numerical experiments illustrate the effectiveness of our method.

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“…Available iteration algorithms are the Newton's method [4-6, 10, 16, 20], the fixed-point iteration method [1,2,8,14,15] and the structure-preserving doubling algorithm [3,7,9,11,17,19].…”

Section: Introductionmentioning

confidence: 99%

A modified large-scale structure-preserving doubling algorithm for a large-scale Riccati equation from transport theory

Guo

2015

Numer Algor

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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%

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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Solving large-scale nonsymmetric algebraic Riccati equations from two-dimensional transport models by doubling

Weng

2021

Journal of Computational and Applied Mathematics

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A modified structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equations from transport theory

Cited by 6 publications

References 14 publications

A modified large-scale structure-preserving doubling algorithm for a large-scale Riccati equation from transport theory

A modified large-scale structure-preserving doubling algorithm for a large-scale Riccati equation from transport theory

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

Solving large-scale nonsymmetric algebraic Riccati equations from two-dimensional transport models by doubling

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