Highly accurate decoupled doubling algorithm for large-scale M-matrix algebraic Riccati equations

关于求解随机连续时间代数Riccati方程的新型不动点型迭代与保结构倍增算法

On Novel Fixed-Point-Type Iterations with Structure-Preserving Doubling Algorithms for Stochastic Continuous-time Algebraic Riccati equations

本文针对随机连续时间代数Riccati方程提出FP-CARE SDA不动点迭代，证明其单调性与R-线性收敛性，并进一步结合修正牛顿法形成FPC-mNT-Lyap SDA算法，数值实验表明其优于现有方法。

Palindromic linearization and numerical solution of nonsymmetric algebraic T-Riccati equations

We identify a relationship between the solutions of a nonsymmetric algebraic T-Riccati equation (T-NARE) and the deflating subspaces of a palindromic matrix pencil, obtained by arranging the coefficients of the T-NARE. The interplay between T-NARE and palindromic pencils allows one to derive both theoretical properties of the solutions of the equation, and new methods for its numerical solution. In particular, we propose methods based on the (palindromic) QZ algorithm and the doubling algorithm, whose effectiveness is demonstrated by several numerical tests

A decoupled form of the structure-preserving doubling algorithm with low-rank structures

The structure-preserving doubling algorithm (SDA) is a fairly efficient method for solving problems closely related to Hamiltonian (or Hamiltonian-like) matrices, such as computing the required solutions to algebraic Riccati equations. However, for large-scale problems in $\mathbb{C}^n$ (also $\mathbb{R}^n$), the SDA with an $O(n^3)$ computational complexity does not work well. In this paper, we propose a new decoupled form of the SDA (we name it as dSDA), building on the associated Krylov subspaces thus leading to the inherent low-rank structures. Importantly, the approach decouples the origi…

Large-Scale Algebraic Riccati Equations with High-Rank Nonlinear Terms and Constant Terms

For large-scale discrete-time algebraic Riccati equations (DAREs) with high-rank nonlinear and constant terms, the stabilizing solutions are no longer numerically low-rank, resulting in the obstacle in the computation and storage. However, in some proper control problems such as power systems, the potential structure of the state matrix -- banded-plus-low-rank, might make the large-scale computation essentially workable. In this paper, a factorized structure-preserving doubling algorithm (FSDA) is developed under the frame of the banded inverse of nonlinear and constant terms. The detailed ite…

求解非对称代数Riccati方程的移位技术

The Shifting Technique for Solving a Nonsymmetric Algebraic Riccati Equation

针对输运理论中的非对称代数Riccati方程，提出一种结合移位技术的保结构加倍算法（SDA），保证二次收敛且无中断，并改进临界情况下的简单迭代算法，显著减少计算步骤。

二重算法用于离散化的贝提-萨尔佩特本征值问题

Doubling algorithm for the discretized Bethe-Salpeter eigenvalue problem

本文提出一种保留结构的二重算法，用于解决离散化的贝提-萨尔佩特本征值问题，通过适当的变换和双凯莱变换避免算法失效，并通过数值结果验证其效率和结构保持性。

SDRE模型的高性能计算与离散卡尔曼滤波用于鲁棒$H_{\infty}$控制

High Performance Computing of SDRE models with Discrete Kalman Filtering for Robust $H_{\infty}$-Controls

针对SDRE控制中在线求解CAREs的计算瓶颈，提出投影通道$H_\infty$公式与离散卡尔曼滤波调度，采用SDA或Newton--Kleinman算法求解，在F-16和四旋翼仿真中验证了高效性与鲁棒性。

求解解耦前向后向随机微分方程的新二阶收敛方案

New Second-order Convergent Schemes for Solving decoupled FBSDEs

本文提出了一种新的二阶收敛算法，用于高效求解解耦前向后向随机微分方程，通过分裂生成器并交替应用显式和隐式方案，提高了计算效率。

利用倍增算法实现组件级准确的流队列计算

Componentwise accurate fluid queue computations using doubling algorithms

本文提出了一种基于倍增算法的组件级准确流队列计算方法，解决了传统算法在计算稳态密度时的精度问题，提供了显式表达式和误差分析，提高了计算的准确性。