Dynamical low-rank integrators for second-order matrix differential equations

被引：2
|
作者：
Hochbruck, Marlis [1 ]
Neher, Markus [1 ]
Schrammer, Stefan [1 ]
机构：
[1] Karlsruhe Inst Technol, Inst Appl & Numer Math, Karlsruhe, Germany
来源：
BIT NUMERICAL MATHEMATICS | 2023年 / 63卷 / 01期
关键词：
Dynamical low-rank approximation; Matrix differential equations; PROJECTOR-SPLITTING INTEGRATOR; TIME INTEGRATION;
D O I：
10.1007/s10543-023-00941-7
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
In this paper, we construct and analyze a new dynamical low-rank integrator for second-order matrix differential equations. The method is based on a combination of the projector-splitting integrator introduced in Lubich and Oseledets (BIT 54(1):171-188, 2014. ) and a Strang splitting. We also present a variant of the new integrator which is tailored to semilinear second-order problems.
引用
收藏
页数：21
相关论文
共 50 条
  • [41] Symplectic integrators for second-order linear non-autonomous equations
    Bader, Philipp
    Blanes, Sergio
    Casas, Fernando
    Kopylov, Nikita
    Ponsoda, Enrique
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 330 : 909 - 919
  • [42] Class of second-order integrators and low-pass differentiators
    American Univ of Beirut, Beirut, Lebanon
    [J]. IEEE Trans Circuits Syst I Fundam Theor Appl, 4 (220-223):
  • [43] Rodrigues' Formulas for Orthogonal Matrix Polynomials Satisfying Second-Order Differential Equations
    Duran, Antonio J.
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2010, 2010 (05) : 824 - 855
  • [44] PROVABLE SECOND-ORDER RIEMANNIAN GAUSS-NEWTON METHOD FOR LOW-RANK TENSOR ESTIMATION
    Luo, Yuetian
    Ma, Qin
    Zhang, Chi
    Zhang, Anru R.
    [J]. 2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2022, : 9057 - 9061
  • [45] Dynamical low-rank approximation
    Koch, Othmar
    Lubich, Christian
    [J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2007, 29 (02) : 434 - 454
  • [46] Oscillation of second-order perturbed differential equations
    Mustafa, OG
    Rogovchenko, YV
    [J]. MATHEMATISCHE NACHRICHTEN, 2005, 278 (04) : 460 - 469
  • [47] Complex second-order differential equations and separability
    Sarlet, W
    Thompson, G
    [J]. APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2001, 11 (05) : 333 - 357
  • [48] Oscillation of Second-Order Neutral Differential Equations
    Li, Tongxing
    Rogovchenko, Yuri V.
    Zhang, Chenghui
    [J]. FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2013, 56 (01): : 111 - 120
  • [49] LOCATION OF ZEROS OF SECOND-ORDER DIFFERENTIAL EQUATIONS
    KOMKOV, V
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 35 (01) : 217 - &
  • [50] Multivalued solutions of second-order differential equations
    A. D. Myshkis
    [J]. Mathematical Notes, 1999, 66 : 719 - 725
12345