個人電腦叢集系統（PC Clusters）為近來被廣泛使用的實驗平臺之一，主要是因為個人電腦叢集系統的價格比一般大型工作站便宜，但卻又擁有很強大的計算能力，並且架設容易。為了評估在個人電腦叢集系統的計算能力以及將它的使用效能最大化，觀察在個人電腦叢集系統上執行處理稀疏資料集（sparse data set）的數值應用程式（numerical applications）的效能是十分有趣的。
稀疏矩陣資料的運算可以應用在許多科學運算的領域中，像是流體力學（CFD）、數值分析（numerical analysis）和電路模擬（circuit simulations）等等。而在目前的一些先進的架構中，處理一般資料的效能和稀疏矩陣的效能似乎有了差距。為了解決這個問題，[Chang 98] 曾經在 IBM SP2 上完成了一套支援 Fortran 90 矩陣內建函式（array intrinsic functions）的平行函式庫。

在這份論文中，我們使用了這套函式庫，完成了兩件事。第一，為了評估電腦叢集系統上處理稀疏矩陣的效能，我們將 [Chang 98] 的函式庫從原先的 IBM SP2 移植到個人電腦叢集系統上，並且做了效能的調整，我們有實驗數據來說明調整後的效能。第二，我們為了讓此函式庫能夠支援更多需求，我們提出了一個有彈性的架構，讓原先的函式庫能夠很容易的支援像是 SuperLU 的數值函式庫。我們的實驗平台是在國家高速電腦中心所提供的八個節點的個人電腦叢集系統上。

PC-based networks of clusters, abbreviated to PC Clusters, have become an important research testbed recently, as their competitive computing powers, inexpensive costs, scalability, and fast interconnections among CPUs are considered. In order to evaluate the computing power of PC Clusters and maximize their performance, it is very interesting to observe the performance results of numerical applications on sparse data sets on PC Clusters. [Chang 98] has designed and implemented a parallel sparse library supporting array intrinsic operations of Fortran 90 on IBM SP2. In this thesis, we have accomplished two results. First, we extend the sparse library developed by [Chang 98] from IBM SP2 to PC Clusters and tune the performance of library on PC Clusters. We will report the performance results in this case. Second, we present a flexible framework to extend the support of the sparse library towards direct numerical solvers such as SuperLU and Cholesky factorization. Our experiments were done on the 8-node PC Clusters at National Center for High-Performance Computing of Taiwan.

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