数值分析重点内容总结

一绪论 ..............................................................................................................................................2 1.1 函数的误差估计及有效数字问题（5） ...........................................................................2 1.2、函数求值的误差估计 ......................................................................................................3 算法的稳定性（1） .................................................................................................................3 1.3. 向量范数的定义及证明（2） .........................................................................................3 二、线性方程组的解法 ...................................................................................................................4 1、GAUSS消元法及列主元消元法的收敛条件及列主元素的求法（5） ..........................4 2.2.1Doolittle和CROUT分解法 ......................................................................................5 选主元的Doolittle分解的公式及主元的计算（3） .......................................................5 2.2.4 追赶法......................................................................................................................6 2.3 矩阵条件数.........................................................................................................................7 4、迭代法.................................................................................................................................7 （1）迭代公式（6） ...............................................................................................................7 （2）收敛性条件（5） ................................................................................................................................................................................10 3.1 幂法与反幂法（10） .......................................................................................................10 3.2 Jacobi法 ............................................................................................................................11 3.3 QR法（3） .................................................................................................................12 3.3.1 豪斯荷尔德矩阵 ....................................................................................................12 3.3.2 矩阵的QR分解： ..................................................................................................12 3.3.3 矩阵的拟上三角化 ..............................................................................................13 3.3.4 带双步位移的QR分解 ..........................................................................................14 四、非线性方程、组的迭代解法 .................................................................................................15 4.1 简单迭代法 ...............................................................................................................15 4.1.1 收敛速度： ............................................................................................................16 4.1.2steffensen迭代法：.................................................................................................16 4.1.3Newton迭代法 ........................................................................................................16 4.1.4 割线法....................................................................................................................17 4.2 非线性方程组迭代解法 ...................................................................................................17 4.2.2Newton法： ............................................................................................................17 五 插值与逼近...............................................................................................................................18 5.1、代数插值........................................................................................................................18 5.2 、Largrange插值 .............................................................................................................18 5.3、Newton形式： ...............................................................................................................18 5.4、插值余项表达式 ............................................................................................................18 5.5 二元函数的插值多项式（2） .........................................................................................19 5.6、Hermit插值及余项（4） ..............................................................................................20 5.7、样条插值........................................................................................................................20 5.7.1 三次样条函数插值 ................................................................................................21 5.7.2 B样条为基地的三次样条插值函数： .................................................................21 5.7.3 三弯矩法求样条插值函数 ....................................................................................23 5.8、三角插值和快速Fourier变换 ........................................................................................25 5.8.1FFT..........................................................................................................................25 5.8.2 快速FFT.................................................................................................................26