Abstract: 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 H-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.

Key words: Precondition, USSOR iterative method, Comparison theorem

摘要： 在预条件矩阵[WTHX]P=I+R[WTBZ]下,提出了新的USSOR迭代法。通过矩阵理论,证明了在非奇异[WTHX]M-矩阵和非奇异H-矩阵下该预条件[WTBZ]USSOR迭代法收敛，并给出了非奇异[WTHX]M-矩阵下预条件[WTBZ]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。

关键词: 预条件, USSOR迭代法, 比较定理