llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllst.files/editdata.mso"> 00-01学年计算方法试题

计算方法试题(00)

2001.1

一、利用Newton法求解下列方程组:

 

在(11)附近的近似解,迭代二次求

二、给定线性方程组:

 

试利用分解法将系数矩阵A分解为A=LU(其中L为下三角矩阵,U为上三角矩阵)然后求解。

三、已知方程组;

   的解为x1=100,x2=-100;

(1)    计算系数矩阵的条件数。

(2)    ,分别计算残量。本题的计算结果说明了什么?

四、设给定线性方程组:

(1)       讨论Jacobi迭代法与Gauss-Seidel迭代法的收敛性。

(2)       对收敛的方法,取初值,迭代两次,求出

五、给出函数表:

    

         xi

0 

1

2

F(xi)

1

2

1

F’(xi)

 

 

-1

且已知F(x)[02]4阶连续可导,求F(x)3Hermiter插值多项式。

六、用最小二乘法求异形如y = a + bx2的经验公式拟合以下数据:

   

xi

19

25

31

38

44

yi

19.0

.32.3

49.0

73.3

97.8