Abstract
In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.
Highlights
The primal goal of this paper is to study the iterative methods of the linear systems: Ax = b, (1)
In 2008, Shou et al [7] have showed that the reconstruction of epicardial potentials (EPs) from body surface potentials (BSPs) can be characterized as an ill-posed inverse problem and geometric errors in the ECG inverse problem will directly affect the calculation of transfer matrix A in (1)
In order to obtain the convergence results, we give some wellknown results which will be used in the proof of Theorem 7 as follows
Summary
In the field of biomedical engineering, Deo et al [6] have mentioned that the cardiac electrical activity can be described by the bidomain equations and pointed out that the numerical solution of partial differential equations (PDEs) associated with bidomain problems often leads to (1). They have proposed a novel preconditioner for the PCG method to solve (1) and a cheap iterative method such as successive overrelaxation (SOR) to further refine the solution for a desired accuracy. The solution of (1) is very important in scientific computing
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
