预条件USSOR迭代法及比较定理

摘要

在预条件矩阵P=I+R下,提出了新的USSOR迭代法.通过矩阵理论,证明了在非奇异M-矩阵和非奇异H-矩阵下该预条件USSOR迭代法收敛,并给出了非奇异M-矩阵下预条件USSOR迭代法与经典USSOR迭代法的比较性定理,揭示了该预条件加快了USSOR迭代法的收敛速度,最后用数值例子验证了定理的正确性.%Under the preconditioned matrix P=I + R, the new USSOR iterative method was put forward. By the theory of matrix, it proved the convergence of the preconditioned USSOR iterative method when the coefficient matrix is a M-matrix or an if- matrix, gave a comparison theorem between the preconditioned USSOR iterative method and the classic USSOR iterative method when the coefficient matrix is a M - matrix, and disclosed precondition iterative method accelerates the convergence speed of the USSOR iterative method. Then a numerical example was used to demonstrate the validity.