Fast enclosure for a matrix inverse square root

被引：6
|
作者：
Miyajima, Shinya [1 ]
机构：
[1] Gifu Univ, Fac Engn, Gifu 5011193, Japan
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 467卷
关键词：
Matrix function; Matrix inverse square root; Numerical enclosure; Verified computation;
D O I：
10.1016/j.laa.2014.11.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A fast algorithm for computing an interval matrix containing the inverse square root of an n x n matrix A is proposed. This algorithm utilizes numerical spectral decomposition of A and requires only O(n(3)) operations. The principal property and uniqueness of the contained inverse square root can moreover be verified by the proposed algorithm. Numerical results show the effectiveness and efficiency of this algorithm. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：116 / 135
页数：20
相关论文
共 50 条
  • [1] Fast Differentiable Matrix Square Root and Inverse Square Root
    Song, Yue
    Sebe, Nicu
    Wang, Wei
    arXiv, 2022,
  • [2] Fast Differentiable Matrix Square Root and Inverse Square Root
    Song, Yue
    Sebe, Nicu
    Wang, Wei
    IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2023, 45 (06) : 7367 - 7380
  • [3] Fast Inverse Square Root Based Matrix Inverse For MIMO-LTE Systems
    Mahapatra, Chinmaya
    Mahboob, Saad
    Leung, Victor C. M.
    Stouraitis, Thanos
    2012 INTERNATIONAL CONFERENCE ON CONTROL ENGINEERING AND COMMUNICATION TECHNOLOGY (ICCECT 2012), 2012, : 321 - 324
  • [4] ON THE COMPUTATION OF A MATRIX INVERSE SQUARE ROOT
    SHERIF, N
    COMPUTING, 1991, 46 (04) : 295 - 305
  • [5] POLYNOMIAL PRECONDITIONING FOR THE ACTION OF THE MATRIX SQUARE ROOT AND INVERSE SQUARE ROOT
    Frommer, Andreas
    Ramirez-Hidalgo, Gustavo
    Schweitzer, Marcel
    Tsolakis, Manuel
    Electronic Transactions on Numerical Analysis, 2024, 60 : 381 - 404
  • [6] A Fast FPGA Based Architecture for Computation of Square Root and Inverse Square Root
    Hasnat, Abul
    Bhattacharyya, Tanima
    Dey, Atanu
    Halder, Santanu
    Bhattacharjee, Debotosh
    PROCEEDINGS OF 2ND INTERNATIONAL CONFERENCE ON 2017 DEVICES FOR INTEGRATED CIRCUIT (DEVIC), 2017, : 383 - 387
  • [7] A Modification of the Fast Inverse Square Root Algorithm
    Walczyk, Cezary J.
    Moroz, Leonid, V
    Cieslinski, Jan L.
    COMPUTATION, 2019, 7 (03)
  • [8] Square Root and Inverse Square Root Computation Using a Fast FPGA Based Architecture
    Hasnat, Abul
    Dey, Atanu
    Halder, Santanu
    Bhattacharjee, Debotosh
    JOURNAL OF ACTIVE AND PASSIVE ELECTRONIC DEVICES, 2018, 13 (2-3): : 135 - 147
  • [9] A one parameter method for the matrix inverse square root
    Lakić S.
    Applications of Mathematics, 1997, 42 (6) : 401 - 410
  • [10] A one parameter method for the matrix inverse square root
    University of Novi Sad, Technical Faculty Mihajlo Pupin, 23000 Zrenjanin
    Applic and Math, 6 (401-410):
12345