For an upper bound of the spectral radius of the QHSS (quasi Hermitian and skew-Hermitian splitting) iteration matrix which can also bound the contraction factor of the QHSS iteration method,we give its minimum point ...For an upper bound of the spectral radius of the QHSS (quasi Hermitian and skew-Hermitian splitting) iteration matrix which can also bound the contraction factor of the QHSS iteration method,we give its minimum point under the conditions which guarantee that the upper bound is strictly less than one. This provides a good choice of the involved iteration parameters,so that the convergence rate of the QHSS iteration method can be significantly improved.展开更多
Based on the quasi-Hermitian and skew-Hermitian splitting(QHSS)iteration method proposed by Bai for solving the large sparse non-Hermitian positive definite linear systems of strong skew-Hermitian parts,this paper int...Based on the quasi-Hermitian and skew-Hermitian splitting(QHSS)iteration method proposed by Bai for solving the large sparse non-Hermitian positive definite linear systems of strong skew-Hermitian parts,this paper introduces a parameterized QHSS(PQHSS)iteration method.The PQHSS iteration is essentially a two-parameter iteration which covers the standard QHSS iteration and can further accelerate the iterative process.In addition,two practical variants,viz.,inexact and extrapolated PQHSS iteration methods are established to further improve the computational efficiency.The convergence conditions for the iteration parameters of the three proposed methods are presented.Numerical results illustrate the effectiveness and robustness of the PQHSS iteration method and its variants when used as linear solvers,as well as the PQHSS preconditioner for Krylov subspace iteration methods.展开更多
基金the National Natural Science Foundation (No.11671393),China.
文摘For an upper bound of the spectral radius of the QHSS (quasi Hermitian and skew-Hermitian splitting) iteration matrix which can also bound the contraction factor of the QHSS iteration method,we give its minimum point under the conditions which guarantee that the upper bound is strictly less than one. This provides a good choice of the involved iteration parameters,so that the convergence rate of the QHSS iteration method can be significantly improved.
基金the China Scholarship Council(No.202208625004)the National Natural Science Foundation of China(No.11501272)Natural Science Foundation of Gansu Province of China(No.20JR5RA464).
文摘Based on the quasi-Hermitian and skew-Hermitian splitting(QHSS)iteration method proposed by Bai for solving the large sparse non-Hermitian positive definite linear systems of strong skew-Hermitian parts,this paper introduces a parameterized QHSS(PQHSS)iteration method.The PQHSS iteration is essentially a two-parameter iteration which covers the standard QHSS iteration and can further accelerate the iterative process.In addition,two practical variants,viz.,inexact and extrapolated PQHSS iteration methods are established to further improve the computational efficiency.The convergence conditions for the iteration parameters of the three proposed methods are presented.Numerical results illustrate the effectiveness and robustness of the PQHSS iteration method and its variants when used as linear solvers,as well as the PQHSS preconditioner for Krylov subspace iteration methods.
