**ROCEWEA. matrix square root**

# Title of paper:
*
***A new stable and avoiding inversion iteration for computing matrix square root**

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

**Tips:** If you find any bug in our files, please contact us: Feng Wu: Email:
vonwu@dlut.edu.cn