矩陣相乘不論在科學上和工程上都是一個基本的應用程式。而叢集電腦是一種新型態的高速計算電腦平台。在此論文中，我們提出一個在叢集電腦上有效率的利用資料分割與資料區域性減少矩陣相乘計算時間的演算法。在叢集電腦上計算矩陣相乘需要考慮兩個影響效能的因素。第一是如何分割資料給處理器減少處理器之間的通訊，第二是利用資料區域性的特性減少處理器計算時快取記憶體與記憶體之間的資料搬移。在本論文中，我們考慮這兩個因素來減少計算矩陣的時間。在資料分割方面，我們提出了兩個方法來分析並減少處理器之間的傳數資料量。此外，我們也提出了如何利用資料區域性的特性來加快矩陣相乘的效能。由數據結果得知，我們的演算法比原始的矩陣相乘演算法節省了40%到50%的執行時間。我們也針對在叢集電腦上計算與通訊之間的關係做分析與評量。 Parallel computer is an important architecture to calculate scienti c and engineer- ing problems. PC cluster is a new computing platform of parallel computer. Low cost and high computation capabilities are the characteristics of PC clusters. This thesis evaluates the performance of matrix multiplication on a PC cluster. Matrix multiplication on a PC cluster should consider two important factors. One is to distribute data to processors to reduce interprocessor communication and the other is to optimize cache utilization to reduce data movements between cache and main memory. As a result, the thesis takes these two factors into consideration and pro- poses two communication-free data distribution schemes: totally duplicate scheme and partially duplicate scheme to totally eliminate interprocessor communication for matrix multiplication. Moreover, the e ect of cache size on matrix multiplication is analyzed as well. Experimental results also show the e ciency of the proposed methods.
