边值问题离散方程组的Jacobi迭代法的多种存储格式实现
摘 要
本论文针对边值问题的离散方程组，设计了多种存储格式的 迭代法，并利用 语言实现了算法。分成3个部分：第1部分是对边值问题的`描述，并对边值问题利用5点差分格式进行了离散，得到了其离散代数系统 。在论文的第2部分，介绍了大型稀疏矩阵 的3种存储格式：满矩阵存储格式、半带宽存储格式和按行压缩稀疏存储格式，并实现了在3种存储格式下的线性代数方程组 的求解。同时将 迭代法、超松弛（ ）迭代法与之比较。论文的第3部分，用1个例题来进行说明。数值实验表明：在 迭代法的多种存储格式中，按行压缩稀疏存储格式存储量最少，半带宽存储格式的存储量少于满矩阵存储格式，且半带宽存储格式耗时比满矩阵存储格式要少很多。 迭代法、 迭代法比 迭代法的迭代次数少， 迭代法的迭代次数最少。
关键词: 迭代法； 迭代法； 迭代方法；半带宽；按行压缩稀疏存储
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
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