北航数值分析计算实习报告一

1、航空航天大学数值分析计算实习报告第一大题学院：自动化科学与电气工程学院专业：控制科学与工程学生姓名：学号：教师：电话：完成日期：2015年11月6日航空航天大学BeijingUniversityofAeronauticsandAstronautics实习题目：第一题设有501x501的实对称矩阵A,bca其中,501a二(1.64-0.024i)sin(0.2i)-0.64e/(i二1,2,501),b二0.16,c=0.064。矩i阵A的特征值为九,(i=1,2,501)，并且有i九X!12501I九1=minI九I1i501求九,九和九的值。1501s九一九2求A的与数卩=九+k一1最接近

2、的特征值九(k=1,2,-,39)。k140ik求A的(谱数)条件数cond(A)?和行列式detA。说明：1在所用的算法中，凡是要给出精度水平的，都取8=10-12。选择算法时，应使矩阵A的所有零元素都不储存。打印以下容：(1)全部源程序；(2)特征值九,九,九，九(k=1,2,.,39)以及cond(A),detA的值。1501sik2采用e型输出实型数，并且至少显示12位有效数字。、算法设计方案1、求九,九和九的值。1501s由于XX!,1九1=mini九I，可知绝对值最大特征值必为九和九TOC o 1-5 h z12501s1i501i1501其中之一，故可用幂法求出绝对值最大的特征值

3、X，如果X=0,则X1=X，否则X=X。将矩阵A进行一下平移：501A=A-XI(1)对A用幂法求出其绝对值最大的特征值X，则A的另一端点特征值X或X1501为X+X。X为按模最小特征值，IX|=minIXI，可对A使用反幂法求得。ss1i501iX_XTOC o 1-5 h z2、求A的与数卩=X+k-501一i最接近的特征值X(k=1,2,.,39)。k140ik计算X(i=1,2,.,501)-卩，其模值最小的值对应的特征值X与卩最接近。因ikkk此对A进行平移变换：A=A-卩I(k=1,2,39)(2)kk对A用反幂法求得其模最小的特征值X，则X=X+卩。kkkkk3、求A的(谱数)条

4、件数cond(A)2和行列式detA。由矩阵A为非奇异对称矩阵可得：cond(A)2=IXmaxX3)min其中X为按模最大特征值，X为按模最小特征值，通过第一问我们求得maxmin的X和-可以很容易求得A的条件数。s在进行反幂法求解时，要对A进行LU分解得到。因L为单位下三角阵，行列式为1,U为上三角阵，行列式为主对角线乘积，所以A的行列式等于U的行列式，为U的主对角线的乘积。算法实现1、矩阵存储原矩阵A为一个上、下半带宽都为2的501X501的带状矩阵，由于矩阵中的0元素太多，如果分配一个501X501的空间保存矩阵的话会浪费很多空间。因此，为了节省存储量，A的带外元素不给存储，值存储带元

5、素，如下C矩阵所示：000bcbcbcbcbC=aaaaaa(4)123499500501bbbbb0cccc00C是一个5X501的矩阵，相比A大大节省了存储空间，在数组C中检索矩阵A的带元素a的方法是：ijA的带内元素a二C中的元素c(5)iji-j+s+1,j2、幂法幂法迭代公式如下：任取非零向量ueRnnk1=IUI|0k-1k-12TOC o 1-5 h zy=u/耳(6)k-1.k-1k-1u=Aykk-1卩=yTukk-1k其中limP=九，不断迭代当IP-Pl/lPl时即可认为其满足精度要kkk1kkTa求，令九=Pk在程序中计算u=Ay时，根据A矩阵的特点，简化如下：kk-1

6、7）(I)-.Iy(1)+by+cyu(2)=by(1)+C32(2)y(2)+by(3)+cy(4)u(500)-cy(498)+by(499)+Cy(500)+by(501)3500u(501)-cy(499)+by(500)+Cy(501)3501u(i)=cy(i-2)+by(i-1)+C3.(i)y(i)+by(i+1)+cy(i+2)(i=3,499)3、反幂法反幂法迭代公式如下：任取非零向量ueRn叮叽0k-1k-12y=u/耳（8）k1k1k1Au=ykk-1卩=yTuJkk-1k1当k足够大时，X。sPk在求解Au=y时，可先对A进行Doolittle分解，由于A是带状结构，

7、kk-1所以分解出的L、U也是带状结构，利用C矩阵进行Doolittle分解并求向量u的算法如下：（1）作分解A=LU对于k=1,2,n执行：c:=c一cckj+s+1,jkj+s+1,jkt+s+1,ttj+s+1,jt=max(1,kr,js)9）j=k,k+1,min(k+s,n)c:=(c刃cc)/cik+s+1,kik+s+1,kit+s+1,ttk+s+1,ks+1,kt=max(1,ir,ks)i=k+1,k+2,min(k+r,n)由于C语言中数组下标是从0开始的，所以在程序中矩阵元素c的下标都减1。后来存放中间向10)(2)求解Ly=b,Ux=y(数组b先是存放原方程组右端向

8、量,量y,在程序中b和y都保存在数组y501中。)b=b-迟cb(i=2,3，,n)iiit+s+l,ttt=max(1,i-r)x=b/cnns+1,nmin(i+s,n)x=(b乙cx)/c(i=n1,n2,1)iiit+s+1,tts+1,it=i+1求出u后,其他部分与幂法求解相同。k三、结果分析实验表明，本程序中，初始向量u=L,u，,u对结果影响较大，合适501x112501的初始向量对得到正确的收敛结果比较重要，如表1是不同初始向量的情况下的得到的部分结果。（实验结果截图见附录）u501x1九1迭代次数九501迭代次数u=11-2.080981085337e+0001599.72

9、4634099378e+000381u=u=112-2.080981085338e+0001609.724634099378e+000381u=u=11400-9.208553159496e+0005359.724634098908e+000573u=u=11461-9.953978978965e+0003509.724634098840e+000592u=u=11462-1.070011361509e+0016749.724634098772e+000611u=1462-1.070011361502e+0013119.724634098772e+000611u=1481-1.07001136

10、1501e+0013049.724634098772e+000611u=u=1-1.070011361502e+0013439.724634098772e+000611462501u=u=1-1.070011361502e+0013439.724634098772e+00061115011,2,501b-1.070011361502e+0013439.724634098772e+000611表1不同初始向量对应的九1和九501及其迭代次数由表1可以得到如下结论：不同的初始向量对本程序的九1影响大，对九501没有影响，都能保证收敛到正确值。初始向量中必须保证U462U501中至少有一个为1才能保

11、证九1收敛到正确值。初始向量非零值的多少和大小对迭代次数并没有明显影响。为解决初始向量对程序的影响，可以先对A做平移变换再求四、实验程序#include#include#includestaticdoubleb=0.16,c=-0.064;#definePrecision1e-12voidcopy(doubleb501,doubley501);doubledianji(doublex,doubley);/计算两个向量积voidInitMatrix(double*p);/InitMatrixAdoubleNeiJi(doublea,doubleb);/get2数voidget_y(double*

12、y,double*u);/getyvoidget_u(double*u,double*y,double*a);/getuvoidInitu(double*p);/初始化初始向量udoubleGet_Fabs_Eigenvalue(double*a,double*u,int*iterations)；/循环迭代得到绝对值最大特征值voidA_sub_minI(double*a,doublemin);/A-min*IvoidInitC(doubleC5501)；/初始化数组CvoidDoolittleC(doubleC5501,intn,ints,intr)；/进行Doolittle分解intmin

13、(inta,intb);/取返回a,b最小值intmax(inta,intb)；/求最大值voidDoolittle_getx(doubleC5501,doubley501,doubleu501,intn,ints,intr);doubleGet_min_Eigenvalue(doubleC5501,double*u,intn,ints,intr,int*iterations);doubledetA(doubleC5501)；/求A的行列式structFinalValuedoublemin；/特征值最小值doublemax；/特征值最大值doubleabs_min；/模最小特征值doublea

14、bs_max；/模最大特征值doubledetA；/A的行列式doublecond2；/A的条件数intmin_iterations；/最小值迭代次数intmax_iterations；/最大值迭代次数intabs_min_iterations；/求绝对值最小的迭代次数；intmain()FinalValuemain_num=0,0,0,0;doubletemp；/两值交换中间变量inttemp1;doubleu501=0；/,y501；/为u0赋初值doubleNorm_u=0；/数doubleC5501=0；InitC(C)；/初始化Cinti=0,*iterations；Initu(u)

15、；iterations=&main_num.min_iterations；main_num.min=Get_Fabs_Eigenvalue(C2,u,iterations)；/将求得的绝对值最大特征值放到min变量中main_num.abs_max=main_num.min；A_sub_minI(C2,main_num.min)；for(i=0；imain_num.max)temp=main_num.min；main_num.min=main_num.max；main_num.max=temp；temp1=main_num.min_iterations；main_num.min_iterati

16、ons=main_num.max_iterations；main_num.max_iterations=temp1；printf(最小特征值为：%.12e,迭代次数为：dn,main_num.min,main_num.min_iterations)；printf(最大特征值为：%.12e,迭代次数为：dn,main_num.max,main_num.max_iterations)；/*以下利用反幂法求解模最小的特征值*/InitC(C)；/初始化CInitu(u)；DoolittleC(C,501,2,2)；main_num.detA=detA(C)；iterations=&main_num.

17、abs_min_iterations；main_num.abs_min=Get_min_Eigenvalue(C,u,501,2,2,iterations)；main_num.cond2=fabs(main_num.abs_max/main_num.abs_min)；printf(绝对值最小特征值为：%.12e,迭代次数为：dn,main_num.abs_min,main_num.abs_min_iterations)；printf(A的行列式为：.12e；,main_num.detA)；printf(A的条件数cond(A)2为：.12en,main_num.cond2)；/*以下利用反幂法

18、求与数列Uk中元素最相近的特征值*/doubleUk39；/保存Uk的值并保存与Uki最接近的入doubleB39；intdiedai；iterations=&diedai；for(i=1；i=39；i+)Uki-1=main_num.min+i*(main_num.max-main_num.min)/40；InitC(C)；Initu(u)；for(intj=0；j501；j+)C2j-=Uki-1；DoolittleC(C,501,2,2)；Bi-1=Get_min_Eigenvalue(C,u,501,2,2,iterations)；Bi-1+=Uki-1；printf(”卩-2d=%-

19、3.12e,与卩%-2d最相近的特征值入=%-3.12en,i,Uki-1,i,Bi-1)；return0；doubledetA(doubleC5501)inti=0；doublee=1；for(i=0；i501；i+)e*=C2i；returne；voidInitMatrix(double*p)for(inti=1；i=501；i+)*p=(1.64-0.024*i)*sin(0.2*i)-0.64*exp(0.1/i)；p+；voidInitu(double*p)for(inti=1;i=501;i+)if(i=500)*p=0;else*p=1;p+;/*p=1;voidA_sub_mi

20、nI(double*a,doublemin)for(inti=1;i=501;i+)*a=*a-min;a+;doubleNeiJi(double*a,double*b)doublee=0.0;for(inti=0;i501;i+)e=e+(*a)*(*b);a+;b+;returne;voidget_y(double*y,double*u)doubleNorm_u=sqrt(NeiJi(u,u);for(inti=0;i501;i+)*y=*u/Norm_u;y+;u+;voidget_u(double*u,double*y,double*a)u0=a0*y0+b*y1+c*y2;u1=b*

21、y0+a1*y1+b*y2+c*y3;for(inti=2;i499;i+)ui=c*yi-2+b*yi-1+ai*yi+b*yi+1+c*yi+2;u499=c*y497+b*y498+a499*y499+b*y500;u500=c*y498+b*y499+a500*y500;voidInitC(doubleC5501)inti;for(i=2;i501;i+)C0i=-0.064;C4i-2=-0.064;for(i=1;i501;i+)C1i=0.16;C3i-1=0.16;for(i=1;i=501;i+)C2i-1=(1.64-0.024*i)*sin(0.2*i)-0.64*exp

22、(0.1/i);doubleGet_Fabs_Eigenvalue(double*a,double*u,int*iterations)doubley501,B_k0=0,B_k1=0;doublewucha;inti=0;while(1)+i;get_y(y,u);get_u(u,y,a);B_kl=NeiJi(y,u)；/是否判断B_K1是否为0?wucha=(fabs(B_k1-B_k0)/(fabs(B_k1);/getwuchaif(wucha10000)printf(迭代次数超长，请更改初始向量n)；break;elseB_k0=B_k1；*iterations=i；returnB_

23、k1；doubleGet_min_Eigenvalue(doubleC5501,double*u,intn,ints,intr,int*iterations)doubley501=0,B_k0=0,B_k1=0；doubleb501=0；/储存y值的中间向量doublewucha；inti=0；while(1)+i；get_y(y,u)；copy(b,y)；/保护y向量Doolittle_getx(C,y,u,501,2,2)；copy(y,b)；B_kl=NeiJi(y,u)；/是否判断B_K1是否为0?wucha=(fabs(1/B_k1-1/B_k0)/(1/fabs(B_k1)；/ge

24、twucha/wucha=(fabs(B_k1-B_k0)/(fabs(B_k1)；/getwuchaif(wucha10000)printf(迭代次数超长，请更改初始向量n);break；elseB_k0=B_k1；*iterations=i；return(1/B_k1)；voidDoolittle_getx(doubleC5501,doubley501,doubleu501,intn,ints,intr)inti,t;doublee;for(i=2;i=n;i+)e=0;for(t=max(1,i-r);t=1;i-)e=0;for(t=i+1;t=min(i+s,n);t+)e+=Ci-

25、t+s+1-1t-1*ut-1;ui-1=(yi-1-e)/Cs+1-1i-1;voidcopy(doubleb501,doubley501)for(inti=0;i501;i+)bi=yi;voidDoolittleC(doubleC5501,intn,ints,intr)intk,j,i,t;doublee;for(k=1;k=n;k+)for(j=k;j=min(k+s,n);j+)e=0;for(t=max(max(1,k-r),j-s);t=k-1;t+)e=e+Ck-t+s+1-1t-1*Ct-j+s+1-1j-1;Ck-j+s+1-1j-1=Ck-j+s+1-1j-1-e;if(

26、k=n)break;for(i=k+1;i=min(k+r,n);i+)e=0;for(t=max(max(1,i-r),k-s);t=k-1;t+)e=e+Ci-t+s+1-1t-1*Ct-k+s+1-1k-1;Ci-k+s+1-1k-1=(Ci-k+s+1-1k-1-e)/Cs+1-1k-1;intmin(inta,intb)if(a=b)returna;elsereturnb;附录：部分实验程序截图1、u=1,1,1x501D:VC6_C+NurnericalAnalyiislDebugNumericalAnalysisl.exs2、u=1,2,5011501x13、u=1,0,0】50

27、1x1rU她WHHII加圍I卿Mb此HIM帼山疆|0：二芯旦八特征值为：2.为：2.772786141752e+lia；=-1.7BbS4U7W57iye+WWkl,-一丄.9070032613丄匕十000,-1.195S5994G4B3C600,=-9.旧041956fiSGF；2e-BO1,=f.0527918?2473e-001.=-3.101388076294e-001,=-1.499B42801155e-002,与卩7=2.801419516063e-001,)口8=5.?52823312242e-001,-|95I1iihXZ卩4I15kl6卩？hXBRRR9R1RR7r+RRH为

28、:9.724634099378e+000,i失代次数668886923785e-002,ft诩近的叩近的诩近的呵诉的吗近的冃近的珅g近的峠冃近的烂目近的堆目近的忖piP2P3卩4P5P610-8.704227108421e-001,|lll=l.l&3O9S43e*0S0,”1112=1.4阳刃04西时张询叽气kl113=1.755843849696e*000,13w14=2.050984229314e*000,114#kll5=2.346124608931e*000,kllSw|lb=2.bl2b4?b4!?e*Ma(!J,ll-lbw117-2.936405368丄卩丄7星|.l18-3.

29、2315157477850*000,|.l18*|J.19=3F；2fifiSfi1与口19暑|120=3.821826507021e*000,|120kl21=4.1169&6886639e*000,与口21最22=4.412107266257e*000,122口乂3=4.?M7U17b如皿咖U占口U3葺|24=5.002388B25492e*000,25-5.29?528d05113c-000,口25毘|l2t=5.592G&a?S472Be*000,|l2遏|127=5.887809164346e*000.H|127*kl28=6.182949543964e*000,kl28kl29=6

30、.478089923582e*000,kl29#kl30=6.773230303199e*000,|13B#hX31=7.Wb3/W62l/ePS：L量32-7.3G3G110G2435e0师,二J卩陀毘|.l33-7.65865143053c*000,|.l33*kl34=7.9537?1821671e*000-134*kl35=8.248932201289e*000,1135#kl36=8.54407258090?e*000,kl36#37=8.839212966525e*000,I37w|UH=y.134Jb334M14ae*HWW,卩期葺獻数为：21cond2:7.7971871599

31、03e+0011X=-1.7bB52L；W4J7bae+Ml!JU1.487964308096k+008tX-1.194709975C3GC-000iX=-9.n96SR1：X=-&_044688812665e-0011X=-3.091270273591e-001LA=-2.238082545211e-002k=2.645ie4233525e-001XXkkkk近白门：近的它近的峙豔近的耳近的峙彳正直正宜征宜征賣征-直flIIq正直征宜征宜征宜.逬昭#止近的瑠正近的瑠正-近的嚅正-X.kkkXXXXkkkA.、=5.46575664673丄亡一00丄-8.51?G29217832e0Q1=9.

32、?78750G2e948e-001=9.97fl7RnRSRnR-Rni=1.73?9464584ee+000=1.73?94644584ee+000=2.23bl358823e+000=2.a3bl3b3M23e+W(!JW-2.236丄35T388玄-2.23tl2Gd3e822c+000=?.S21420419102+000=3.52143019108e+000=3.52143019108e+000=3.52143019108e+000=5.144584028615e+0B0-5.1445e4028G15c003=5.1445e4Q28Gle*0Q3=5.144584e28615e003

33、=5.1445e4Q28&15e009=6.528021%5584e000=6.528021Q65584e009=b.b2UM21ldb5btt4e+杪杪皿-G.5280216GC84e0OS近的喻正近制#正-?.&1439080G407C*000=7.9A44fiASaH9fi+HfiH=7.964466535889e+000k=7.?644E6535889e+000X=8.870882321966e*000h=H.7UHKlVb6eUMIdk-8.B70882321?66e-t0034、u=h,o,J501x13=-7.125782?651?4e+000,|17=-6.6151648723

34、286+000,P-8=-6.104545379481e+000,|193U-2U3U4(J-5吐k!8|15R-6IX-8值I-8.G48CGC0G5194C309/宜工-9.2E九寸九575+000.22176249575e-B02!D：VC6C+NumeriralAnaly5islDebugNumericalAnalysisl.exeITIEtD；1.0?00113ClElGc001my正值为；9-7246346987720*000,对播梟小转征逍切2勺行別帀片I：2-77271417R3A411S卩1U-2|13=-1.31394949222fie+BR1,=-9.f；7SR7A229

35、4n9fi+liiRR.=-9.16B257536562e+B00,=-B.S57638843715e+606,=-B.1470201508fc8e+B00,=-7.S36491458021e+60S,10=-5.593926fc8fc634e+606,|X10|111|X12|113|X14|115|X16|117|X1B|.l19腆鑫2-呵肅苗彳E珂近的12=-4.b7ZbSV3W0V4We与(J-13=-4.UbaW?W60W3e+HWB,14=-3.55451915246e+e00,P丄53.9498332224O0e*606,与1G-2.53021452?553e606,(J-17-

36、3.01J575S3G7OGc606,18-1.S08977143859c-606,|-l19?.?83584510123c-G01,1120=-4.877?975HlG54e-601,5N21=2.2S739l4fifi144e-ffi2,与卩最彳kL22=R.497f；272RR-Rfi1.与kl2=1.R4411f；2R37Sft+fifiRP与口殆曇;kl24=1.554735013222c+060.口跆曇;kl25=2.0&53537B6069e+060口25審;126=2.575972398916+060,与口恋最”kl27=3.0865910917636+060,与皿1?最;kl

37、28=3.5?720?784fc09e+060,与128#kl29=4.1978284774566+060,与129w:kl30=4.618447170303c+060,与130#31=5.1290658631506+06032=b.bJytB455bW7e+VA,卩32豊八hX33=b.lbM3W32444e+MBW小33最八34=6.660921941690c+000,与卩3皐刀hX35=7e+060,小35星：；36-7.6825?327384e+000,与卩3石皐：；37-8.172778020231e应0,与P3T曇:38-8.70339&713B7ec06

38、0,38:W近的:近側近的：近的寸近的峙征殖的坤彳正近的物近的峙衽近的:：近的怜近的；近的怜近的近的近的近的近的血勺岀勺近羽近的近的:巒；mi妙；6H丘仕校数共；:数wndS、；!为：4.794F；24271*002.=-1.01H3934fl31F；F?+fR1X=-1niR394iSR+fini入=-1.018293403315e+001X=-8.652284007898e+000入=-8.6E228007898e+000X=-8.652284007898e+000入=-?.207083654072b+000A=-?.2e?083654072e+000A=-6.066103226595e+

39、000A=-6.0E6103226595e+000X=-b.WfcblWJabbi/bE+UtlUA=-4.bU522431bbk)VBX=-4.bb2231bbk)?eA=-3.5542丄丄2丄575丄E+00目人3.5542丄丄2丄575丄匕*000X-2.52G436459138ti909X-2.52G430459138c-000X-2.52G430459138d003X1.S3738E573473c+000=-5.2222225945285-901.22F；92Re-0f1-_2朋药裔94用貼-0町1.flF2R9fl9A2A9R+llRfl1.465061771296e+0002.0

40、81232695829e+3002.718922410569e+0002.718922410569e+0003.63690E0Q1100B+3004.091378510451E+0004.60303S378279e+0005.1E9998268651e+000b.HWVHbHbbMe也醐b.25b211WbaV2E+l!JMl!6.706874576024b+9097.2538774-18丄+0007.624C23960361e+3O9.225226O14S50E309ffix洁入值hfx值扎038.0S7539595ei0e-001-21HRS717437r-R31644B7163619e-

41、00164935677413e-001695?7562128e+000421670347E4e+000144184610E6e+6003Vb4V8W45Ve+(!10(!J688&0?4?460e+6003757043758GeG0O92G756Gt454cG0Oiaei039?lle+Q0Q生7fiS41lRfi1fi+lilHR14923&686(2e+Q00472766905E6e+000255?9571178e+00093877448126e+00017111714235e+000759331646?le*60054200344575cG0Q三7、u二u二二u二112400*D：VC6

42、_C+NumeriralAnaly5islDebugNumsricalAnaJysisl.exegift对值;卩JklaU3H4U5吐k!8朗k!10J-ll冲J-13kl-14卩丄5卩丄&征值为；9.20855315949GC000,迭代慎数共；535笹值为；9-?2624696968c+000,7:G73.最小暮征逍为；-5.55791079423Be-303,为；加A的条件数condB,-U.bl?37bltHbe+H0B,-2.1086979375?5e+e00,-.5352?8256134e*606,近划近坏近知近的?近划近側J-17-1.lG1.948574G74e606,18-G

43、.88G188?32143e601,hX19-2|.l20|l21|l22k!24U-25k!26U27k!28kl29k!30kl31k!32J-33434J-353bJ-3738.1528?2117542c6012.580404G970G9C-0G1,7.31370i511t6Oe-061,1.204S9?a22t2te+060,1.67SB29Rl40Sf.f?+OB(i少一佔1詰对眄4弘+01徊2.6246888?7O0te+0603.0?891855846te+0603.57134823992fce+0604.044677921387c+0604.5180076B2847e+060,

44、口29最4.9?1337284307e+060，一貝5.4S4666965?67e+0605.937996647227c+0606.411326328687e+060,465141141476+114,”7.3b7y5b?lbW7e+WBW,31313730676+00,8.394S45054527e+060,8.777?74735987e+060,1_G5Ga271&425e*S02-R.R94HRfinA7RR+flR3-7.812994457614b+009-7.374686607908e+000-6.8254797085056+000-6.2e8139637311e+000-5.907

45、811600224b+000-5.397186969431e+000-4.953431292001B+000-4.461457971735e+000-4.064286817756b+009-J.54Jy41bb7abe+atll!J-2.5fc2db212?ba?e+Utll!J-2.丄丄旦目-1.630336496814c+303iX-1.1595551190G1K000X-G.8S8SlG0G5435e901X-2.132588?902e901Xx值人xxxxXXAAAAA近的埠正值近的峙征值近的峙征莓近的峙征值近咤專f!Es目近散峙与|121最7；目近為寺与|122烹谒近的坤.与卩旳最胡

46、近的峙”与口74最;目近的:寺占U25wfl诉摘:寺诉加喏：s.S.5：3098、另冒二二1，其余都为038:疇im=-1.01844?2Z24e+(d01,=-V.b?887b23Vbe+UHHHJ.=-V.lb2b?53bb4!?e+(!10(!l,=-B.b57b3H43?M3e+m,=-B.147KJZWlbOMbbe+l!ll!l,T.636401458013e+S0S,=-7.1257827S5163e+000,=-6.615164072317e+000,=-6.104545379470e+000,回D:VC6_C+NumerkalAnalyEislDebugNumericalAn

47、alysis!.exe勺：-1.973011361509e+01,迭(弋】文;勺：9.724634098772e*60e,去弋说畫近的特征值近的特正值近的喻正宜近的峙正直入T近的特正值=-8-近的特正值入近的特正值入近的持正值入近的特正道A=-6.近的转正直近的筍正直iI丄胸丽科诉R归暹稠尸的最珂迂的”U殆量甬迂的占4量珂迂的占卩亦量明迁的占卩必量珂迂的与1127量珂迁的与I曲匮珂迂的与10還珂迁的与Z噓:珂迂的.曇珂迂的Id*000,与卩盟昜:冃迂的P盟蹇珂迂的与g遢珂迂的小35最甬迂的豺:674攵対：&115579167?423Oe-003,运彳片衣数则:702.7727861-11752

48、e*丄丄&|丄1|山IM|丄|Xt|X8I丄9.9252042739丄5e*目03k=-1.Ul2VJ4l!l3315e+WltlX=-!?.b8111tlb44W4Ke+0U(!l172b72423y2Se+W0(!l.EbH4MU?KVUe+MUMUV34NdNN675e+MUU=-7.S590E407E92e+000=-7.119684648E91e+0O0=-S.S11764339397e+000366103226595e+0O0A=-5.585101052E28e+000A=-5.114083529812e+000X=-4.57887217686Ee+000_=-4.39647S92

49、626e+000直X=-3.554211215751e+000=-3.041090018133e+000=-2.533970311130e+0003e323S7e?563e+0O0=-l.503557611227e+00053558606007Ee-001B702E738e5Se-0Ol=2.231736249575e-002=S.2417742fiA9fi-Rni=1.BR2R9R9fi2fi9ft+RnR=1.SH97ll=-5.083307993777e+000,|lllw；kll2=-4.5?2689330?31e+000,|X坨最;ll3=-4.062070638384e+000,|

50、X13w；kll4=-3.55145191523Be+000,j|114w；15=-3.040833222391e+000,|115w；kll6=-2.530214529545e+000,i|X167kll?=-2.019595836698e+000,|117f41118=-l.588977143852e+000,i|X18|119=-9.983584510050e-001.iU-19|I120=-4.8?7397581585e-001|121=2.28?893468800b-002.口戈戈=_胆497馭巧34血-则|12=1.04411|J24=1.?；F；471F；ai22Br+W(JIW

51、2=2.0fiS337WfiO74p+B(i|(i|J2f.=2.?；7972193921R+WflW|l27=3.0S6591091767b+0G0,1128=2.597239784614+3Q01129=4.107S2S477460B*0晅|.l30-4.618447173307c+3G01-131-E.129065363153C+0G0,|32-E.t39G84S5G000IJ.33-C-15B30324881GC3G0,|34-C.tG0921?41G?3c3G0hX35-7.171540G34539e-060,”3C-7.t8215932738Ge-000,I3C：IJ.37-6.1

52、92778020232k-060,37.|38-E.7033?6713079ti+0G0,.214B15405725匕十000,二j小3,最9、u4621，其余为07P12P1JP14P15P16J17P18卩19i卩1J=-4.Mb2M7MbMHMJNe卩14=-3.551451915194e+0丽115=-3.046833222349e+30kll6=-2.530214529504s+0丽m?=-2.01959583fc659e+000=-9.678876229331e+000=-9.168257E3fc487e+30=-H-佔泅尺4*4恥胸=-S.1*?威01耳”9*时耐=-7.6364

53、61457952?*0607.1257627651070+360-G.G151G40722G2c0D0-G.10-154537?4i8e-060i冃近时aJ20=-4.79751247e-Bfi1”匕1121=2.2S7S93472013e-002,21|-122-5.33497t275t49c-001,号-I22#23-1.044116320410c006,23曇24-1.554735013255c006,24皐-2.9653537B6B9?e*006,25曇=2.575972398944c*006,J-26S口2?=3.UabblMlVUe27W2B=J.bV72Wy7B4b34e閱量hi

54、29=4.107828477479e*000,J,29#30=4.61847170323e000,30|133=6.150303248858e+000,33#|15U=R.ffiB9219417R1r询胴与1i?；=7.171MBfi4548e5J.IF；#112t=7.Sa2159227?92e*006,5丨比皋|-l37-8.1927760202370*006,-I37#38-8.70339C713082c006,J-38#冃近竹哇E匚冃近的用正値冃近的坤征莓冃近的贷厂日近的镭征1冃匕土汇洁D:VC6_C4+NumericslAnalE：ilDbugNumericalAnalysis：l.

55、&xe=-1.0189494922186+001,1118=-1.508977143814e+360.|119=-9.9RR4SH9A9Rft-lillii1”hil05.5?3926686573e*060,卩ll=-5.0B3307?93728e+060,卩12=-4.b?2bV3WH883e-2.311743e30007c-G01-8.lC?218531G?c601-1.4C5BG177129Ge600工-2.060330460274t+6Q0工=2.521802793?94e+608工=J.b2143U41VlUNe+UUZ=4.091378510451e+000A=4.6B303537

56、8279e+000Z=5.144584028S15e+000工=5.3E212?077120e+000=6.2E62119?5892e+00B工=A.ARHR4H92112fl+fiRn7.=7.341lF；fi159979p+B0O)=7.7171117142?te+600?.-8.315923327090c+600工一藝.7759331&4G91C608?”-8.972341252413c600铲最小特征值划m，迭佔抄软为：Ju堆代次数为：54gcondfi垃为：4.794524270984e询02亠X=-1.0182934033156+001X=-1.0182934033156+001X

57、=-9.172672423928e+000X=-RA22R4fia7RgRft+flRflX.=-H.WRfin292S1Rfl7ft+Hn=-7.7O070379GG54e+000X7.70070370GtS4c+OB0X-G.G117G4339357c-000X-G.182G7977G712tBBB入6.18267077B712t+OS0X=-5.丄丄4O8J529812e+OO0X=-4.bU522431bbe+UMUX=-3.艸粘叫昭342牡+uuuA=-3.98950?323424e+B00A=-3.428982295215e+000X=-2.526439459138e+000X=-

58、2.526430459138e+B00X=-1.623292192195e+B00X=-9RFR9H19S92F2fi-nRlX=-乩加323亦94曰恥一胴1:-1.W7WUlldblbO2e+0(!ll:YJ吃叫即丫昭+醐叫2317362495756-002,iii用近的轉正用近的特正用近的转正用近的特正咽近的特正用近的特正帘近的特正用近的特正珀近的特正用近的特正用近的特正冯近的特正11用近的弟正沟近跑电止_目近茁特彳7=2.231736249575e-602屢4书征值J:丁勺徐为:2.7?278&141752e+118Pl10、u=462u=i，其余为0501近的近的近的近的近的近的近首勺

59、近的近的近的近的近的近的诉的件ficond2g：近的:写I吨嚨靈专I12Sig近的力“弓卩戈9最涓近的肚UH=4.A1R4471:?阴2缶+胴九三口汕最泪近的力；343.11：佔S.9R19147SAr+RH1gX=-1.018293403315e+001IX=-9.58570742586Be+0004k=-9.172672423928e+000重扎=-8.604250985fc83e+000追A=-8.086B29281887e+000渲h=-?.700700706654e+000值=-7.3W5Ub/7?11MVe+WWH/宜X,=-6.bll?b43393?7e+0tltl酋X,=-6.

60、182679770712e+060宜汇5.74535445849丄匕十0阳道k5.114383529812c00/宜X4.d34B08347304c+060/宜X=-g.989509222424e+060/宜X.=-q.12H9R22?F；215e+Rfif/宜k=7541HARIRI喈k=-2.526430459138e+000盾k=-2.10877378228le+060值k=-1.6232921?2195e+000h=T.558?03959252e-0011代=-5.3332325?4528e-001A=-l.78814606?732e-601A.dll74JH3Wl!lW7e-Wl!l