【摘要】：基于預(yù)處理修正的Hermitian和skew-Heimitian分裂(PMHSS)迭代方法和交替方向的PMHSS(ADPMHSS)迭代方法的思想,本文提出了一種新的迭代方法來求解一類復(fù)對稱線性系統(tǒng),即參數(shù)化PMHSS(P2MHSS)迭代方法.在本文中,我們不僅從預(yù)處理矩陣的角度給出了 P2MHSS迭代方法的參數(shù)選取方法和計算公式,還分析了該方法的收斂性質(zhì),并證明了其在一定條件下對任意的初始向量都會收斂到該線性系統(tǒng)的精確解.最后,我們用數(shù)值算例驗證了 P2MHSS迭代方法的可行性和有效性.
[Abstract]:In this paper, a new iterative method is proposed to solve a class of complex symmetric linear systems, i.e., the parametric PMHSS (P2MHSS) iterative method, based on the pre-processing modified Hermitian and the skew-Heimitian splitting (PMHSS) iterative method and the alternating direction PMHSS (ADPMHSS) iterative method. In this paper, we not only give the parameter selection method and calculation formula of the P2MHSS iterative method from the angle of the pre-processing matrix, and also analyze the convergence property of the method, and prove that any initial vector will converge to the exact solution of the linear system under certain conditions. Finally, we use a numerical example to verify the feasibility and effectiveness of the P2MHSS iterative method.
【學(xué)位授予單位】：蘭州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O241.6

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本文編號：2456317