1、有關(guān)三對角矩陣的數(shù)值分析摘要3 對角矩陣是1 類很重要的特殊矩陣, 在數(shù)學(xué)和物理學(xué)中有廣泛的應(yīng)用 . 文章將根據(jù) 3 對角矩陣的特征，用待定系數(shù)法求解 3 對角線性方程組的數(shù)值解，并與常用的 lu分解法從理論分析和數(shù)據(jù)實(shí)驗(yàn)兩方面進(jìn)行比較 , 結(jié)果表明 , 兩者的時間復(fù)雜性前者稍差 , 而精度兩者則相當(dāng) , 最后寫出兩者的 c程序并運(yùn)行結(jié)果 . 接下來用 1 種簡單和容易實(shí)現(xiàn)的方法求出 3 對角矩陣的行列式，再利用其逆矩陣可以分解成兩個很特殊的矩陣的乘積，給出 1 種算法實(shí)現(xiàn) 3 對角矩陣的逆的簡便計(jì)算。關(guān)鍵字： 3 對角矩陣；待定系數(shù)法；數(shù)值解；行列式；逆abstractthe tridiag

2、onal matrix is a kind of matrix that with important special,it has widespread applications in mathematics and physics.in this paper,based on the characteristic of the tridiagonal matrix,the method of hypothetical coefficient is used for the numerical solution of tridiagonal system of linear equation

3、s,this method will be compared with the lu resolving method through theory analysis and data experiment,compared the two methods,we will find the latter is better than the former in time complexity slightly ,but the precision is matched with each other,finally write the c procedures for the two meth

4、ods and get results. the next part,an easy algorithm will be used to compute the determinant of the tridiagonal matrix.the inverse can be divided into two so specialmatrices that we can compute out the explicit inverse via an algorithm.keywords:tridiagonal matrix;numerical solution;determinant;inver

5、se目 前言11 兩 求解3 角方程 的數(shù) 方法21 1 引入 21 2 待定系數(shù)法求解3 角方程組 21 3 lu分解法求解 3 角方程 71. 4 算法性能分析 9 2 關(guān)于 3 角矩 的行列式 122 1 引入 122 2 方法提出 122 3 算法性能分析 133 3 角矩 逆的數(shù) 解法 153 1 引入 153 2 算法推 及 153 3 程序與數(shù) 例子 17 結(jié)論 20 參考文獻(xiàn) 20 致謝 21摘要3 角矩 是 1 很重要的特殊矩 , 在數(shù)學(xué)和物理學(xué)中有廣泛的 用 . 文章將根據(jù) 3 角矩 的特征，用待定系數(shù)法求解3 對角 性方程 的數(shù) 解，并與常用的lu分解法從理 分析和數(shù)據(jù)

6、兩方面 行比 , 果表明 , 兩者的 復(fù) 性前者稍差, 而精度兩者 相當(dāng) , 最后寫出兩者的 c程序并運(yùn)行 果 . 接下來用 1種 和容易 的方法求出 3 角矩 的行列式，再利用其逆矩 可以分解成兩個很特殊的矩 的乘 ， 出1 種算法 3對角矩 的逆的 便 算。關(guān) 字：3 角矩 ；待定系數(shù)法；數(shù) 解；行列式；逆abstractthe tridiagonal matrix is a kind of matrix that with important special,it has widespread applications in mathematics and physics.in this

7、 paper,based on the characteristic of the tridiagonal matrix,the method of hypothetical coefficient is used forthe numerical solution of tridiagonal system of linear equations,this method will be compared with the lu resolving method through theory analysis and data experiment,compared the two metho

8、ds,we will find the latter is better than the former in time complexity slightly ,but the precision is matched with each other,finally write the c procedures for the two methods and get results. the next part,an easy algorithm will be used to compute the determinant of the tridiagonal matrix.the inverse can be divided into two so special matrices that we can compute out the explicit inverse via an algorithm.keywords:tridiagonal matrix;numerical solution;determinant;inverse目 前言 11 兩 求解 3 角方程 的數(shù) 方法21 1 引入 21 2 待定系數(shù)法求解3 角方程組 213lu分解法求解3 角