**ROCEWEA. matrix cosine**
# Title of paper:
*
***An algorithm based on adaptive filtering technique for the computation of large-scale matrix cosine being
nearly sparse**

Authors: *Jiqiang Hu, Feng, Wu, Li Zhu, Yuelin Zhao, Wanxie Zhong*

The scaling-squaring method (SSM) s for computing the matrix cosine function has been developed for many years, but
it is not applicable for the large-scale sparse matrix as it requires more memory and higher computation cost than
they are actually needed.

In this paper, we analyze the localization phenomenon of the matrix cosine by two concepts, the real-bandwidth and
the epsilon-bandwidth, and find that for the matrix cosine, there exists an approximate sparse matrix cosine under
the given error tolerance. The existence of this approximate sparse matrix cosine provides the mathematical basis
for the application of filtering technique. Then, a new algorithm which combines the filtering technique with the
SSM is proposed. The error changes in the iterative process of the proposed algorithm is discussed, and an adaptive
filtering threshold based on the error analysis is given.

Numerical experiments show that the new algorithm can greatly improve the computational efficiency of large-scale
sparse matrix cosine function with high accuracy and less memory, compared with several existing numerical
algorithms.

## Code

**Type: **MATLAB code

**File: **cosfilt.rar

**Contents: **

The algorithm proposed in this article: cosfilt.m;

And the filtration algorithm ‘filtoutA4.m’ proposed in ‘High-performance computation of large sparse matrix
exponential’.

27 test matrices: A1.mat ~ A27.mat

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