Theory of numerical analysis.docx - 1 解线性方程:...

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1. 解线性方程: Gauss LU (求逆,求特征值) 2. 插值 : lagrange ,有理多项式,三次样条 3. 线性最小二乘法: 正规方程 ,奇异值分解 4. 矩阵本征值问题: Jacobi householder QR ,幂次法 5. 非线性方程(组)求根: 二分法 + 迭代法 迭代: Newton (x k+1 =x k -f(x)/f’(x) Newton-Raphson) 割线法 (x x+1 =x k -f(x)/s(x),s(x)=(f(x k )-f(x k-1 ))/(x k -x k-1 )) 错位法, Ridders Brent’s (划界 + 二分 + 反插值), M N 元: Broyden Newton-Raphson 终极思想:方程线性化再来进行迭代, F(x+h)=f(x)+f’(x)h 6. 优化问题 黄金分割法,抛物线法, Newton BFGS (拟牛顿法),最速降落法, CG (共轭梯度) Powell 7. 常微分方程的初值问题的数值解法: 欧拉方法,后退欧拉, 化导数为插上 数值积分 taylor 开) runge-kutta 法(高阶), 线性多步法, 8. 非线性最小二乘法: Gauss-newton MRQ 9.
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