A filtering technique for the matrix power series being near-sparse

TL;DR

This paper introduces a filtering-based algorithm for near-sparse matrix power series that enhances computational efficiency while maintaining accuracy, outperforming traditional methods and MATLAB's built-in functions.

Contribution

The paper proposes a novel filtering technique for the matrix power series that improves sparsity and efficiency without sacrificing accuracy.

Findings

The new algorithm achieves similar accuracy to the original Paterson-Stockmeyer scheme.

It is more efficient than the original scheme and MATLAB's built-in codes for near-sparse matrices.

The method effectively balances error control and computational savings.

Abstract

This work presents a new algorithm for matrix power series which is near-sparse, that is, there are a large number of near-zero elements in it. The proposed algorithm uses a filtering technique to improve the sparsity of the matrices involved in the calculation process of the Paterson-Stockmeyer (PS) scheme. Based on the error analysis considering the transaction error and the error introduced by filtering, the proposed algorithm can obtain similar accuracy as the original PS scheme but is more efficient than it. For the near-sparse matrix power series, the proposed method is also more efficient than the MATLAB built-in codes.