Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let the system matrix of a linear system be p-cyclic and consistently ordered. Under the assumption that the pth por of the associated Jacobi matrix has only non-positive eigenvalues, it is known that the optimal spectral radius of the SOR-k iteration matrix is strictly increasing as k increases from 2 to p. ,  first show that the optimal parameter of the SOR-k method as a function of k is strictly increasing. The behaviour of the spectral radius of the SOR-k method (for fixed parameter) is then studied.
['Liancheng Wang', 'Jiehua Zhu', 'Xiezhang Li']
I am writing a research paper on a idea The SOR-k method for linear systems with p-cyclic matrices
[{"from": "human", "value": "I am writing a research paper on a idea The SOR-k method for linear systems with p-cyclic matrices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let the system matrix of a linear system be p-cyclic and consistently ordered. Under the assumption that the pth por of the associated Jacobi matrix has only non-positive eigenvalues, it is known that the optimal spectral radius of the SOR-k iteration matrix is strictly increasing as k increases from 2 to p. ,  first show that the optimal parameter of the SOR-k method as a function of k is strictly increasing. The behaviour of the spectral radius of the SOR-k method (for fixed parameter) is then studied."}]