## Homotopy understanding of iterative methods.(English)Zbl 1097.65511

The author shows that solving a linear system $$Ax=b$$ by iterative methods, such as the Jacobi, Gauss-Seidel, and successive over-relaxation (SOR) methods, can be understood in the setting of homotopy continuation methods, which may provide a new insight into those iterative methods. Based on this new understanding, a condition for the convergence of those iterative methods is presented, which turns out to be equivalent to the traditional one.

### MSC:

 65F10 Iterative numerical methods for linear systems 65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations