Scaled norm minimization method for computing the parameters of the HSS and the two-parameter HSS preconditioners

作者：Yang, Ai-Li^*

来源：Numerical Linear Algebra with Applications, 2018, 25(4): e2169.

DOI：10.1002/nla.2169

• HSS preconditioner
• matrix trace
• parameter value
• preconditioning effect
• scaled norm minimization method

The performance of the Hermitian and skew-Hermitian splitting (HSS) preconditioner for the non-Hermitian positive definite system of linear equations is largely dependent on the choice of its parameter value. In this work, an efficient scaled norm minimization (SNM) method is proposed to compute the parameter value of the HSS preconditioner. In addition, by choosing different parameters for the Hermitian and the skew-Hermitian matrices in the HSS preconditioner, a two-parameter HSS preconditioner is proposed. Moreover, an efficient and practical formula for computing the parameter values of this new preconditioner is also derived by using the SNM method. Numerical examples are illustrated to verify the performances of the HSS and the two-parameter HSS preconditioners when their parameters are computed by the SNM method.

• 出版日期2018-8
• 单位兰州大学