ROCEWEA. matrix pth root

Title of paper: 大规模稀疏矩阵主p次根的快速计算

Authors: Jiqiang Hu, Feng, Wu

The current iterative methods for computing the primary p-th root of matrix A are not suitable for the large-scale sparse matrix as it requires more memory and higher computation cost than they are actually needed.
In this paper, we first designed a new iterative method which completely avoiding using the inverse matrix named “CAIM”. We analyze the convergence and stability of CAIM, the result shows this algorithm is stable. But CAIM is still not suitable for the large-scale matrix. Thus, we added the filtering technique to CAIM, and developed the filtering completely avoiding using the inverse matrix method, shorted as “FCAIM”. Based on the error analysis of the FCAIM, we give a criterion for choosing the fixed filtering threshold, which can greatly optimize the computational efficiency while maintaining high accuracy.
Numerical experiments show that the CAIM is more efficient compared with the algorithm which required inverse matrices and the FCAIM can greatly improve the computational efficiency of the large-scale sparse matrix for computing the primary p-th root of matrix A with high accuracy and less memory, compared with several existing numerical algorithms.

Code

Type: MATLAB code
File: p-th root.rar
File: test_matrices_A1-A20.rar
File: test_matrices_A21-A29.rar
Contents:
The algorithm proposed in this article: FCAIM.m, CAIM.m;
And the filtration algorithm ‘filtoutA4.m’ proposed in ‘High-performance computation of large sparse matrix exponential’.
29 test matrices: A1.mat ~ A29.mat

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