ROCEWEA. matrix square root

Title of paper: Fast computation of matrix square root with sparse approximation

Authors: Li Zhu, Keqi Ye, Yuelin Zhao, Feng Wu, Jiqiang Hu and Wanxie Zhong

In this study, a new stable iterative method avoiding fully matrix inversions (denoted by SIAI) is proposed based on the Newton iteration. The corresponding proof on the numerical stability of the proposed method is given. The selection of the initial matrix for the iteration is also recommended, which broadens the applicable matrix range of the original Newton iteration. The sparsity of the matrix principal square root is also discussed by using the real bandwidth and ε-bandwidth. The analysis shows that there exists a sparser approximate matrix with the similar accuracy for each matrix involved in every iterative step of the SIAI. The filtering technique with an adaptive filtering threshold based on the error analysis is proposed to obtain this sparser approximate matrix. Combining the filtering technique with the SIAI yields the SIAI_F. Numerical examples shows the contributed SIAI is more efficient than the Newton iteration, the DB and the IN method. The proposed SIAI_F can compute the principal square root matrix being nearly sparse efficiently and precisely.

Code

Type: MATLAB code
File: SIAI_F.rar

Contents:
The algorithm proposed in this article: sqrtm_SIAI_F.m;
And 'filt_norm.mexw64' is the filtration algorithm proposed in ‘High-performance computation of large sparse matrix exponential’.
45 test matrices: A1.mat ~ A45.mat

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