In this paper we discuss iterative methods to solve the linear operator equation Au = f, (1) posed on a finite dimensional Hilbert space V equipped with an inner product (?,?)? Here A : V →V is a symmetric positive definite (SPD) operator, f ? V is given, and we are looking for u G V such that (1) holds. The X-Z identity for the multiplicative subspace correction method for solving (1) is introduced and proved in [7]. Alternative proofs can be found in [1, 4]. In this paper we derive the X-Z identity from the auxiliary space method [3, 6]. A basic linear iterative method for solving (1) can be written in the following form: starting from an initial guess u~0, for k = 0,1,2, …
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机译：在本文中，我们讨论迭代方法来解决配备有内部产品的有限维希尔伯特空间V上的线性操作员方程Au = F，（1）（？，？）？这里答：v→v是一个对称的正明（spd）运算符f？ v是给出的，我们正在寻找U g V这样（1）保持。介绍了用于求解（1）的乘法子空间校正方法的X-Z标识，并证明[7]。替代证据可以在[1,4]中找到。在本文中，我们从辅助空间方法[3,6]中得出了X-Z身份。求解（1）的基本线性迭代方法可以以下列形式写入：从初始猜测U〜0开始，对于k = 0,1,2，...
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