摘 要
本論文針對邊值問題的離散方程組，設計了多種儲存格式的 迭代法，並利用 語言實現了演算法。分成3個部分：第1部分是對邊值問題的`描述，並對邊值問題利用5點差分格式進行了離散，得到了其離散代數系統 。在論文的第2部分，介紹了大型稀疏矩陣 的3種儲存格式：滿矩陣儲存格式、半頻寬儲存格式和按行壓縮稀疏儲存格式，並實現了在3種儲存格式下的線性代數方程組 的求解。同時將 迭代法、超鬆弛（ ）迭代法與之比較。論文的第3部分，用1個例題來進行說明。數值實驗表明：在 迭代法的多種儲存格式中，按行壓縮稀疏儲存格式儲存量最少，半頻寬儲存格式的儲存量少於滿矩陣儲存格式，且半頻寬儲存格式耗時比滿矩陣儲存格式要少很多。 迭代法、 迭代法比 迭代法的迭代次數少， 迭代法的迭代次數最少。
關鍵詞: 迭代法； 迭代法； 迭代方法；半頻寬；按行壓縮稀疏儲存
Abstract
Considering the boundary value problem discreted equations, this thesis tried to design a iteration with three memorial formats, and to use fortran language to realize its arithmetic. It is divided into 3 parts: the 1st part is the description of boundary value which is discreted by using 5 point differential format, the algebraic system is get. The 2nd part, 3 kinds of memorial formats for large sparsely matrix are introduced : full matrix memory format, the half band-width memory format and row compressed memory format, the solution for linear algebraic equations in these three memorial formats are realized. And iteration, iteration and Jacobi iteration is compared part too. The 3rd part, Numerical results show that in these memorial formats of Jacobi, row compress sparse memory has the smallest memory quantity, and half-bandwidth memory format’s memory quantity is less than full matrix storage format and it take less time too. The iteration times of iteration and iteration are less than those of Jacobi, and SOR iteration has the least iteration times.
Keywords: iteration; iteration; iteration; half band-width; row compress sparse memory
說明：論文中有些數學符號是編輯器編輯而成，網頁上無法顯示或者顯示格式錯誤，給您帶來不便請諒解。