Parallel solution of large-scale and sparse generalized algebraic Riccati equations

被引：0
|
作者：
Badia, Jose M. [1 ]
Benner, Peter
Mayo, Rafael
Quintana-Orti, Enrique S.
机构：
[1] Univ Jaume 1, Dept Ingn & Ciencia Comp, Castellon de La Plana 12071, Spain
[2] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany
来源：
EURO-PAR 2006 PARALLEL PROCESSING | 2006年 / 4128卷
关键词：
generalized algebraic Riccati equation; Newton's method; generalized Lyapunov equation; LR-ADI iteration; parallel algorithms;
D O I：
暂无
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We discuss a parallel algorithm for the solution of large-scale generalized algebraic Riccati equations with dimension up to O(10(5)). We survey the numerical algorithms underlying the implementation of the method, in particular, a Newton-type iterative solver for the generalized Riccati equation and an LR-ADI solver for the generalized Lyapunov equation. Experimental results on a cluster of Intel Xeon processors illustrate the benefits of our approach.
引用
收藏
页码：710 / 719
页数：10
相关论文
共 50 条
  • [31] Hierarchical node method for solving large-scale sparse linear equations in parallel
    Wang, Yongqing
    Liu, Bin
    ACTA MECHANICA SINICA, 2024, 40 (04)
  • [32] REDUCED BASIS APPROXIMATION OF LARGE SCALE PARAMETRIC ALGEBRAIC RICCATI EQUATIONS
    Schmidt, Andreas
    Haasdonk, Bernard
    ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2018, 24 (01) : 129 - 151
  • [33] An inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations
    Benner, Peter
    Heinkenschloss, Matthias
    Saak, Jens
    Weichelt, Heiko K.
    APPLIED NUMERICAL MATHEMATICS, 2016, 108 : 125 - 142
  • [34] Large-scale discrete-time algebraic Riccati equations-Doubling algorithm and error analysis
    Chu, Eric King-wah
    Weng, Peter Chang-Yi
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 277 : 115 - 126
  • [35] USING LDLT FACTORIZATIONS IN NEWTON'S METHOD FOR SOLVING GENERAL LARGE-SCALE ALGEBRAIC RICCATI EQUATIONS
    Saak, Jens
    Werner, Steffen w. r.
    ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2024, 62 : 95 - 118
  • [36] PARALLEL ALGORITHMS FOR ALGEBRAIC RICCATI-EQUATIONS
    GARDINER, JD
    LAUB, AJ
    INTERNATIONAL JOURNAL OF CONTROL, 1991, 54 (06) : 1317 - 1333
  • [37] Numerical Solvers for Generalized Algebraic Riccati Equations
    Ivanov, I. G.
    Rusinova, R. I.
    APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES, 2009, 1186 : 343 - 351
  • [38] On an iterative algorithm to compute the positive stabilizing solution of generalized algebraic Riccati equations
    Feng, Yantao
    Anderson, Brian D. O.
    CCDC 2009: 21ST CHINESE CONTROL AND DECISION CONFERENCE, VOLS 1-6, PROCEEDINGS, 2009, : 3530 - 3534
  • [39] On the strong solutions of generalized algebraic Riccati equations
    Xin, X
    Mita, T
    SICE '98 - PROCEEDINGS OF THE 37TH SICE ANNUAL CONFERENCE: INTERNATIONAL SESSION PAPERS, 1998, : 791 - 796
  • [40] Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems
    Benner, Peter
    Li, Jing-Rebecca
    Penzl, Thilo
    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2008, 15 (09) : 755 - 777
12345