贵大数值分析上机实习报告

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1、数值分析上机实习报告学院：土建学院专业:学号:姓名:上机实习题一、题目：已知A与b(12.38412,2.115237,-1.061074,1.112336,-0.113584,0.718719,1.742382,3.067813,-2.0317432.115237,19.141823,-3.125432,-1.012345,2.189736,1.563849,-0.784165,1.11234&3.123124-1.061074,-3.125432,15.567914,3.12384&2.031454,1.836742,-1.056781,0.336993,-1.

2、0101031.112336,-1.012345,3.123848,27.108437,4.101011,-3.741856,2.101023,-0.71828,-0.037585A彳-0.113584,2.189736,2.031454,4.101011,19.89791&0.431637,-3.111223,2.121314,1.7841370.718719,1.563849,1.836742,-3.741856,0.431637,9.789365,-0.103458,-1.103456,0.2384171.742382,-0.784165,-1.056781,

3、2.101023,-3.111223,-0.103458,14.7138465,3.123789,-2.2134742.067813,1.11234&0.336993,-0.7182&2.121314,-1.103456,3.123789,30.719334,4.446782(-2.031743,3.123124,-1.010103,-0.037585,1.784317,0.238417,-2.213474,4.446782,40.00001b={2.1874369,33.992318,-25.173417,0.84671695,1.784317,-86.61234

4、3,1.1101230,4.719345,-5.6784392}1.用Household变换，把A化为三对角阵B(并打印B)。2.用超松弛法求解BX=b(取松弛因子3二1.4,対°)二0,迭代9次)。3.用列主元素消去法求解BX=bo二、解题方法的理论依据:1、用Householder变换的理论依据(1)令A0=A,a(ij)l=a(ij),已知Ar_l即Ar_l=a(ij)r(2)Sr=sqrt(pow(a,2))(3)a(r)=Sr*Sr+abs(a(r+1,r))*Sr(4)y(r)=A(r_l)*u®/a®(5)Kr二(/2)*Ur的转置*Yr/a®(6)Q

5、r=Yr-Kr*Ur(7)Ar=A(r-l)-(Qr*Ur的转置+Ur*Qr的转置)r=l,2,,……，n~22、用超松弛法求解其基本思想：在高斯方法己求出x1时，可以加快收敛速度3、用消去法求解用追赶消去法求Bx二b的方法：2H+1TB5S》c迂+

6、二HB5H+二》qlovo"U1OVO-pEn—C1S/&1E+alsdlshi丄2:.&msn(d一s—巳sMs)/(£s+a一s・s—二)9in一2・：・9x〔9vul〔9〕§Hgls・+二+H8Z:・Jr4牺谕曲“艺nclude=maul.IT-^include=stdio.h=^definegeXvoidmain。imsign(douboX)；doublea〔=9n(一2.3X4122二523711061074"1•1123361P二3500407100719J.74230023067001312031743=(2•二5237J9•一±823「3・12543

7、2二-.0123452189736」L5638496.784165r二23483123124厂.1.061074「3・125432・15.567914312384820314541836742「1.05670010336993「1.01003厂P112336工012345312384827・08437400lr3・7418562120236.718286・037585L〒0•二35OC421OC973620314544SS二」9OC9791Oc.0.431637:3•一二223212131417*4317厂(0.718719・一.563849"1OO36742J