【精品】数值分析上机作业

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1、一程序要求:已知A=12.3841202.115237-1.0610741.112336-0.1135840.7187191.7423823.067813-2.0317432.11523719.141823-3.125432-1.0123452.1897361.563849-0.7841651.1123483.123124-1.061074-3.12543215.5679143.1238482.0314541.836742-1.0567810.336993-1.0101031.112336-1.012345

2、3.12384827.1084374.101011-3.7418562.101023-0.718280-0.037585-0.1135842.1897362.0314544.10101119.8979190.431637-3.1112232.1213141.7843170.7187191.5638491.836742-3.7418560.4316379.789365-0.103458-1.1034560.2384171.742382-0.784165-1.0567812.101023-3.111223-0.

3、10345814.7138463.123789-2.2134743.0678131.1123480.336993-0.7182802.121314-1.1034563.12378930.7193344.446782-2.0317433.123124-1.010103-0.0375851.7843170.238417-2.2134744.44678240.00001b=(2.187436933.992318-25.1734170.846716951.784317-86.6123431.11012304.719

4、345,-5.6784392);1.用Householder变换,把A化为三对角阵B(并打卬B).2.用超松弛法求解Bx二b(取松地因子3=1.4,X<0)=0,迭代9次)3.用列主元素消去法求解Bx-bo二.解题算法1.HOUSEHOLDER算法步骤：⑴令Ao-A,aij⑴=dij.已知Ar-1即A!-i=(3ij(r))(2)Sf(£(air(H)2)l/2f=r+l(3)ar=Sr2+

5、ar+i,r

6、SrUr=[0,…，0,a(r>r+

7、,r+Sign(a

8、…，a/T(4)yr=Ar-lUr/«r(5)kr=UrTyr/2ar(6)q.-yr-krU,(7)Ar=AI-i-(qIUrT+UrqrT),r=(l,2,•••,n-2)2.SOR解题算法其基本思想是在高斯方法已求lhx/+1其屮3是超松弛因子，当3>1时，可以加快收敛速度。3.列主元素消去法程序算法对矩阵作恰当的调整，选取绝对值尽量大的元素作为主元素。然后进行行变换，把矩阵化为上三和阵

9、，再进行回代，求出方程的解。三主要程序#include#defineN9main()floate[N+l],f[N+l],xlLN4-l],A0LNJ[N],B[N][N],y[N],u[N],w[N],x0[N];floatx[N],q[N],ql[N],ul[N],ma,al[N],s,s2,k,bl[NJ;staticfloatb[N]={2.1874369,33.992318,-25.173417,0.8471695,1.784317,-86.612343,1.1101230,4.7

10、19345,-5.56784392};inti,j,r,sign;floatA[N][N]={{12.38412,2.115237,-1.061074,1.112336,-0.113584,0.718719,1.742382,3.067813,2031743},{2.115237,19.141823,-3.125432,-1.012345,2.189736,1.563849,-0.784163,1.112348,3.123124},{-1.061074,-3.125432,15.567914,3.12384

11、8,2.031454,1.836742,-1.056781,0.336993,-1.010103}J1.112336,■1.012345,3.12384&27.108437,4.101011,-3.741856,2.101023,-0.71828,-0.037585},{-0.113584,2.189736,2.031454,4.101011,19.897918,0.431637,-3.111223,2.1213