Iterative methods to solve the constrained Sylvester equation

被引：2
|
作者：
Yu, Siting [1 ]
Peng, Jingjing [1 ]
Tang, Zengao [1 ]
Peng, Zhenyun [1 ]
机构：
[1] Guilin Univ Elect Technol, Coll Math & Computat Sci, Guilin 541004, Peoples R China
来源：
AIMS MATHEMATICS | 2023年 / 8卷 / 09期
基金：
中国国家自然科学基金;
关键词：
nonlinear matrix equation; fixed point iteration algorithm; Anderson acceleration algorithm; Thompson distance; ALTERNATING PROJECTIONS; ANDERSON ACCELERATION; RICCATI EQUATION; MODEL-REDUCTION; MATRIX; ALGORITHM;
D O I：
10.3934/math.20231097
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the multiple constraint least squares solution of the Sylvester equation AX + XB = C is discussed. The necessary and sufficient conditions for the existence of solutions to the considered matrix equation are given. Noting that the alternating direction method of multipliers (ADMM) is a one-step iterative method, a multi-step alternating direction method of multipliers (MSADMM) to solve the considered matrix equation is proposed and some convergence results of the proposed algorithm are proved. Problems that should be studied in the near future are listed. Numerical comparisons between MSADMM, ADMM and ADMM with Anderson acceleration (ACADMM) are included.
引用
收藏
页码：21531 / 21553
页数：23
相关论文
共 50 条
  • [21] An iterative algorithm for solving the generalized Sylvester-conjugate matrix equation
    Song, Caiqin
    JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2018, 58 (1-2) : 545 - 566
  • [22] New iterative method to solve the radiative transfer equation
    Vilhena, M.T.
    Segatto, C.F.
    Journal of Quantitative Spectroscopy and Radiative Transfer, 1996, 55 (04):
  • [23] An iterative procedure to solve a class of algebraic Riccati equation
    Stoica, A.
    Berbente, S.
    UPB Scientific Bulletin, Series D: Mechanical Engineering, 1999, 61 (3-4): : 387 - 394
  • [24] A new iterative method to solve a volume integral equation
    de Carvalho, SA
    Mendes, LS
    ITS '98 PROCEEDINGS - SBT/IEEE INTERNATIONAL TELECOMMUNICATIONS SYMPOSIUM, VOLS 1 AND 2, 1998, : 410 - 414
  • [25] Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions
    Xie, Yajun
    Ma, Changfeng
    JOURNAL OF APPLIED MATHEMATICS, 2014,
  • [26] A new iterative method to solve the radiative transfer equation
    Vilhena, MT
    Segatto, CF
    JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, 1996, 55 (04): : 493 - 498
  • [27] Numerical methods for nearly singular constrained matrix sylvester equations
    Ghavimi, AR
    Laub, AJ
    SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1996, 17 (01) : 212 - 221
  • [28] Numerical Methods for Nearly Singular Constrained Matrix Sylvester Equations
    Ghavimi, A. R.
    Laub, A. J.
    SIAM Journal on Martix Analysis and Applications, 17 (01):
  • [29] Distributed Algorithm for Solving Sylvester Matrix Equation via Iterative Learning Control
    Liang, Cong
    Huo, Xuanmin
    Xte, Shizhou
    Wang, Lei
    Li, Juntao
    2023 IEEE 12TH DATA DRIVEN CONTROL AND LEARNING SYSTEMS CONFERENCE, DDCLS, 2023, : 1165 - 1170
  • [30] Numerical Solution of Sylvester Equation Based on Iterative Predictor-Corrector Method
    Iyikal, Ovgu Cidar
    JOURNAL OF MATHEMATICS, 2022, 2022
12345