Abstract

A partially structure-preserving method for sparse symmetric matrices is proposed. Computational results on the permanents of adjacency matrices arising from molecular chemistry are presented. The largest adjacency matrix of fullerenes computed before is that of C₆₀ with a cost of several hours on supercomputers, while only about 6 min on an Intel Pentium PC (1.8 GHz) with our method. Further numerical computations are given for larger fullerenes and other adjacency matrices with n=60,80. This shows that our method is promising for problems from molecular chemistry.

Keywords: Permanent of matrix; Adjacency matrix; Structure-preserving algorithm; Fullerenes

PACS: 02.10.Eb; 02.10.Sp; 81.05.Tp

Article Outline

1. Introduction

2. Algorithms

2.1. Ryser–Nijenhuis and Wilf method (R-NW)

2.2. A hybrid method

2.3. A partially structure-preserving method

3. Numerical results

3.1. The permanents of the adjacency matrices of fullerenes

3.2. Comparison with results before

3.3. Further numerical computation

4. Discussions and conclusions

Acknowledgments

References

Supported by National Science Foundation of China G10228101 and National Key Basic Research Special Fund G1998020306.