矩阵排序的几何方法
A Geometric Approach to Matrix Ordering
摘要：
我们提出了一种递归的方法来划分超图，创建和利用超图几何，适用于众核并行架构。这样的划分然后被用于以递归的有界块对角形式（用于处理器无关的并行LU分解）或递归的分离块对角形式（用于高速缓存无关的稀疏矩阵向量乘法）来带来稀疏矩阵。我们表明，所获得的分区和排序的质量是有竞争力的，通过比较所获得的填充LU分解与SuperLU（具有更好的结果为28个测试矩阵中的8个）和比较切割的大小稀疏矩阵向量乘法与蒙德里安（具有更好的结果为12个测试矩阵中的4个）。新方法的主要优点是其速度：它平均比Mondriaan快21.6倍。
英文摘要：
We present a recursive way to partition hypergraphs which creates and exploits hypergraph geometry and is suitable for many-core parallel architectures. Such partitionings are then used to bring sparse matrices in a recursive Bordered Block Diagonal form (for processor-oblivious parallel LU decomposition) or recursive Separated Block Diagonal form (for cache-oblivious sparse matrix-vector multiplication). We show that the quality of the obtained partitionings and orderings is competitive by comparing obtained fill-in for LU decomposition with SuperLU (with better results for 8 of the 28 test matrices) and comparing cut sizes for sparse matrix-vector multiplication with Mondriaan (with better results for 4 of the 12 test matrices). The main advantage of the new method is its speed: it is on average 21.6 times faster than Mondriaan.
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