A new across-diagonalized preconditioner space based on Sine transform is proposed, and it is proved that the existing diagonalized preconditioner space based on Sine transform is its sub-space.
给出了基于正弦变换的交叉对角化预条件矩阵的构造空间，证明了已有正弦变换基预条件矩阵的构造空间是新的构造空间的子空间。
参考来源 - Toeplitz系统的高效预处理技术和分布式并行算法研究·2,447,543篇论文数据，部分数据来源于NoteExpress
在构造预条件因子时，采用从目标的“几何结构剖分”出发，而不是从“矩阵元素”出发确定“基权函数之间的作用量关系”，这样保证了构造预条件矩阵的计算复杂度仅为O（N）。
The preconditioner is generated from the target's "geometry structure " and not from the "matrix element", which assured the computational complexity for generating the preconditioner is only O(N) .
为了克服这一困难，本文通过引进一个仿射变换矩阵，构造仿射投影既约预条件共轭梯度路径来搜索获得迭代方向。
In order to overcome the difficulties, we introduce an affine scaling matrix, and form the affine scaling reduced preconditional conjugate gradient path to obtain a new accepted step.
首先将有理函数阻抗矩阵插值技术应用于采用预条件器加速的矩量法求解过程。
Firstly, impedance matrix interpolation is incorporated in MoM in combination with the preconditioning technique.
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