本文主要是探討奔騰4處理器與個人電腦叢集計算的最佳化技術，我們針對寫程式時常碰到的五種計算型態，包括向量加乘、向量內積、全矩陣向量相乘、稀疏矩陣向量相乘及全矩陣相乘，來分析奔騰4處理器中的SSE2指令集對運算速度的影響，並由不同的資料量，來觀察記憶體與處理器間的關係，同時與其他不同性能的處理器(AMD Athlon XP及奔騰III處理器)做比較。利用以上稀疏矩陣向量相乘實驗的數據，在個人電腦叢集上對平行有限元素做負載平衡。
　　我們使用包裝、暫存器及區塊的方式來提升運算速度。在向量加乘和向量內積中因資料型態簡單，程式不做unroll，Intel編譯器會以包裝方式及unroll運作而得到最佳結果。在全矩陣向量相乘中程式利用unroll方式來撰寫以充分利用暫存器。稀疏矩陣向量相乘以原來的寫法及全矩陣相乘以jik順序即可得到不錯的結果。在平行處理方面，於負載平衡後有不錯的運算速度。

　　The purpose of this thesis is to study the computation optimization technique on Pentium 4 processor and personal computer clusters. Five commonly used calculating types which are the vector-vector addition and multiplication, vector inner product, full matrix-vector multiplication,sparse matrix-vector multiplication, full matrix-matrix multiplication are studied in this research. We analyze the influences of the SSE2 instruction set on operating speed. Different data amount and the relationshipbetween the memory and the processor are studied. The results are compared with other processors (AMD Athlon XP and Pentium III processors)which have distinct performances. On the personal computer clusters, the results of sparse matrix-vector multiplication are used to do load balance of parallelism in finite element method.
　　Packed data, unroll and block technique are used to increase the computation speed in this research. Because vector-vector addition and multiplication and vector inner product have simple data structures, the Intel compiler can automatically packed data and unroll to produce assembly code even no unrolling in C++ codes. The use of unrolling in full matrix-vector multiplication makes good use of registers which will increase the computation speed. Sparse matrix-vector multiplication in original ways and full matrix-matrix multiplication in jik method have good operating speed. In parallelism of the Jacobi conjugate gradient method, the operating speed after load balance has good performance.

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