Data Analysis and Applications 1

10Evaluation of Stopping Criteria for Ranks in Solving Linear Systems

Linear systems of algebraic equations arising from mathematical formulation of natural phenomena or technological processes are common. Many of these systems of equations are large, the matrices derived are mainly sparse and need to be solved iteratively. Moreover, interpretation is crucial in making decision. Bioinformatics, internet search engines (web pages) and social networks are some of the examples with large and high sparsity matrices. For some of these systems, only the actual ranks of the solution vector is interesting rather than the vector itself. In this case, it is desirable that the stopping criterion reflects the error in ranks rather than the residual vector that might have a lower convergence. In this chapter, we evaluated stopping criteria on Jacobi, successive over relaxation and power series iterative schemes. Numerical experiments were performed and results show that Kendall’s correlation coefficient τ gives good stopping criterion of ranks for linear system of equations.

10.1. Introduction

Sparse and large linear systems of equations are common in many physical applications. In particular, the Internet search engine is one area where such systems are encountered and have been studied intensively. The concepts have been deployed in areas such as social networks, bioinformatics and infectious disease management (Wills and Ipsen 2009). With growing technology, the size of data from these ...