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

2014/07/09 by Pei-Chang Guo, Guo, Peichang
Computer Science · Mathematics · Physics and Astronomy · #15A24 #65F50 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1407.2520

openalex publication_date 2014/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider the large scale nonsymmetric algebraic Riccati equation arising in transport theory, 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 structure-preserving doubling algorithm, which can reduce the flop operations of original SDA_ls by half. Numerical experiments illustrate the effectiveness of our method.

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