数值实验指导书.doc

数值实验指导书
数值实验一
实验名称:非线性方程求根(Solution of Non-linear Equation)
实验目的:掌握二分法、不动点迭代、牛顿迭代法等常用的非线性方程迭代算法;加深对不同算法收敛速度、对初值的依赖性等的认识。
基本要求:应用C语言或Fortran语言及Matlab编程,并上机调试通过;2学时。
算法描述:
计算的二分法(bisection Method):
PURPOSE: To find a solution to F(x)=0 given the continuous function F on the interval [A,B], where F(A) and F(B) have opposite signs
INPUT: endpoints: A,B, tolerance: TOL>, maximum number of iterations N
OUTPUT: approximation solution P or message that the algorithm fails
Step 1 Set I=1
FA = F(A); FB=F(B)
Step 2 While do Steps3-6
Step 3 Set P=A+(B-A)/2; FP=F(P).
Step 4 IF FP=0 or (B-A)/2<TOL THEN
OUTPUT (P) (pleted essfully)
STOP
END IF
Step 5 Set I=I+1
Step 6 IF THEN
Set A=P; FA=FP
ELSE
Set B=P; FB=FP
END IF
Step 7 OUTPUT (Method failed after N iteration)
STOP
2. 计算的不动点迭代(Fixed-Point Iteration):
PURPOSE: To find a solution to given an initial approximation p0
INPUT: initial approximation p0; tolerance TOL; maximum number of iterations N
OUTPUT: approximation solution p or message of fails
Step 1 Set I=1
Step 2 While do Steps 3-6
Step 3 Set (compute )
Step 4 IF THEN
OUTPOT (P) (the procedure was essful.)
STOP
END IF
Step 5 Set I=I+1
Step 6 Set (Update )
Step 7 OUTPUT (Method failed after N iteration)
STOP
3. 计算的牛顿法(Mewton Method):
PURPOSE: To find a solution to given an initial approximation :
INPUT: initial approximation ; tolerance TOL; maximum number of iteration N.
OUTPUT: approximate solution or message of failure.
Step 1 Set
Step 2 While do Steps 3-6
Step 3 Set (*Compute *)
Step 4 If then
Output(p)
Stop
Step 5 Set
Step 6 Set
Step 7 Output (The method failed after N iterations)
(* The procedure was essful *)
Stop.
实验步骤与注意事项:
、Fortran语言或Matlab编写以上三种算法的通用程序。
, 附近的根,比较收敛速度。
,取不同的初值,观察算法对初值的敏感性。
。
:如何比较迭代法收敛的快慢?何为收敛阶数? 如何加速迭代序列的收敛速度?埃特金加速法的处理思想是什么?
数值实验二
实验名称:多项式插值(Polynomial Interpolation)
实验目的:掌握多项式逼近的思想,熟悉Lagrange插值算法,分段低