Chebyshev-type methods and preconditioning techniques

Hou-Biao Li, Ting-Zhu Huang, Yong Zhang, Xing-Ping Liu, Tongxiang Gu

Abstract: Recently, a Newton’s iterative method is attracting more and more attention from various fields of science and engineering. This method is generally quadratically convergent. In this paper, some Chebyshev-type methods with the third order convergence are analyzed in detail and used to compute approximate inverse preconditioners for solving the linear system Ax = b. Theoretic analysis and numerical experiments show that Chebyshev’s method is more effective than Newton’s one in the case of constructing approximate inverse preconditioners.