实验结果表明了该文所提出的基于线性表出的非奇异循环变换局部性优化方法是有效的。

The experimental results show that the linear expressing based approach for optimizing locality using non-singular loop transformations presented in this paper is effective.

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首先，定义了一个函数类的集合，该集合中元素的导数可以由该集合中的元素线性表出；

First of all, a function set is defined, in which the derivative of the elements can be linearly represented by the elements;

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该文提出了一种新的利用非奇异循环变换来优化程序局部性的局部性优化方法，即基于线性表出的循环变换。

The paper presents a new locality optimization approach using non-singular loop transformations to optimize programs' locality, namely linear expressing based loop transformations.

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正基于此，本文进一步以矩阵和向量为工具对解法进行优化，使通过初等行变换后经线性表出就可以产生结果。

Because of this, this paper optimizes the solution further regarding matrix and vector quantity as tools, and it can produce the result through linear expression after elementary line change.

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正基于此，本文进一步以矩阵和向量为工具对解法进行优化，使通过初等行变换后经线性表出就可以产生结果。

Because of this, this paper optimizes the solution further regarding matrix and vector quantity as tools, and it can produce the result through linear expression after elementary line change.

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