2025年数值解析关键任务作业挑战

YN结束本次作业所使用的编译环境为：Visualc++6.0doubleA[10][10],rr[10][10],qq[10][10],rq[10][1//对矩阵A进行初始化，赋值{{A[i-1][j-1]=sin(0.5*i+0.2A[i-1][i-1]=cos(i+1.2*i)*}//定义函数对矩阵A进行拟上三角化{intsgn(doublea);doubled,c,h,t,tr,u[10],p[10],q[10],w[10];{for(i=r+2;i<10;i++)t=t+(A[i]{{}}for(i=0;i<10;i++)sum=sum+p[i{{A[i][j]=A[i][j]-w[i]*u[j]-u[i]}}}}}}//sgn子程序intsgn(doublea){}//计算A的特性值的函数(书本P6311步)inttezhengzhi(){voidqmk(doublemk[10][10],intm,doublems,doublemt);//申明求mk的函数voidQR(doublemk[10][10],intm);//申明对mk进行qr分解的函数detdk=A[m-1][m-1]*A[m][m]-A[m-1][fb=-1.0*(A[m-1][m-1]+A[m{}{s1_r=(-1.0*fb+sqrt(s2_r=(-1.0*fb-sqrt(}}{}{if(-1e-12<A[m-1][m-2]&&{{}elseif(m==-1)}{{mt=A[m-1][m-1]*A[m][m]-}}{doubletmp_sum;{{for(k=0;k<=m;k++)tmp_sum+=A[i][k]*}}for(i=0;i<=m;i++)mk[i][}//对mk做QR分解并得到A(k+1)的函数{doubleur[10],vr[10],pr[10],qr[10],wr[10],tmp_dr,tmp_vr,tmp_pr,tmp_qr,tmp_tr,dr,ctmp_ir=tmp_ir+(mk[i]{234for(i=r;i<=m;i++)tmp_dr=tmp_dr+mk[i][r]*mfor(i=r+1;i<=m;i++)ur[i]=mktmp_vr=tmp_vr+mk[j][itmp_pr=tmp_pr+A[j][itmp_qr=tmp_qr+A[i][j}}for(i=0;i<=m;i++)tmp_tr=tmp_tr+pr[i]for(i=0;i<=m;i++)wr[i]=qr[i]-tr{{A[i][j]=A[i][]-wr[i]*ur[j]-ur[i]}}}{}{}voidtranslation(doub{{{}}}//列主元的高斯消元法求解特性向量{for(k=0;k<9;k++)/*选主元并消元*/{mk=k;//记录最大组员的行号for(i=k;i<10;i++)//*选择第K列主元素{{}if(mk!=k)/*将第K列主元素换行到对角线上*/{{}}{A[i][j]=A[i][j]-mik*A[k}}/*回代求解*/x[9]=b[9]/A[10-1][1{{}}}{{{}{}{}}while(fabs(beita2-beita1)>=fabs(beita2)*exp(-1for(m=0;m<10;m++)xy[m]}//主程序{{{}}printf("矩阵A各个特性值的实部及虚部为：\n\n");{}printf("经带双步位移的QR分解后的矩阵为：\n");{{if(-1.0e-12<A[i][j]&&A[i][j}}{{{}{}}}1.通过上三角化后的矩阵经过上三角化后的矩阵为255889387184e-8016.83259944534e-11.51886895646939998e+008-6.388578124485e-001-4.15487338868395-0819.783997%21285e-0822.557763574.08836·B.88e·8-1.21695343e+8-4.11683513396+E⁸1+e⁸-41.3W⁷583821e+e⁸1.883691775ke-1-4.246335358369e-8817.988955239384-0821.68819928869e-.08368e-B.8e:·88.88838e-81.5681262522-·88.12584937515e-14.421756832232-1-1.588616128136718-01-2.7365958588920-801-7.32446835-081-6.7099254814498-0812.5446199298821893682e-0811.19587191495e-0811.9298618e-014.9882594688e-011.1376916837762.0089008-88.8808908-80.00930+08B.0808+088.0008008-08B.08900-088.0808908-087.031672187e-B⁸11.582188688475e-BP¹3.86259461422.88888+8B.88B8908+88.88888+08B.808+88.088-8B.8388e+88.088e+B⁰84.843887682783e-B⁰13.992777995-8.e-001-9.e-002-1.e+000-7.e-0011.e-001-2.e+0002.e+0001.8e+0003.e-0012.e-0012.e+0001.8e-0011.e+000-6.e0.e+0001.e+000-1.5e+000-1.e+000-6.e-001-2.e+000.e+0000.e+000-1.e+000-0.e+0000.e+0000.e+0001.e+0008.e-0014.e-001-3.e-0024.e-0010.e+0000.e+0000.e+0000.e+0000.e+000-7.e-001-2.e-002-90.e+0000.e+0000.e+0000.e+0000.e+0000.e+000-7.e-001第1个特征值为：(3.383839617436e+880,a.098888888888e+888i)第2个特征值为：(-2.323496218212e+880,8.938405177208e-881i)第3个特征值为：(-2.323496218212e+880,-8.9304851?7200e-881i)第4个特征值为：(1.577548557113e+088,a.000808808880e+080i)第5个特征值为：(-1.484839822259e+080,a.888808808888e+888i)第6个特征值为：(-9.805309562982e-881,1.139489127438e-801i)第?个特征值为：(-9.805309562902e-Q81,-1.139489127430e-Q01i)第8个特征值为：(9.355889878188e-O⁰1,0.000eene⁸8800e+000i)第9个特征值为：(6.360627875746e-Q81,a.80080880888Ce+080i)第10个特征值为：(5.650488993581e-882,a.0008Be008088e+000i)5218517e-802-1.882578788827e+088-4.886268122088BP⁸e·-2.184744213e+8-2.3615279847Ke+8-1.4561256863c-02-4.7641314:21.81639532183e·8-2.318975622He5516812783e-081-6.537876947738e-B⁰13.227152128265524e-BE]-4.154391785514-082-1.861198124719-801.04875636749-01-22887e-BR¹-5.962368585233e-081-4.9115922718343047e-822.98478806855e-081-3.57W³9888185223188e-811.877411851833e-8011.36825651900ke+Bee6.368511809728e-012.737834413363e-0810+02.45769935855-05.6516496536请证值3.3309617406e-对应的特征向量为：(2.3838426916e4.363067W26e-+82.96232952853.41钳锄4924-3.1922812991e+3.4685172特征值1.57548559113e+对应的特征向量为：(5.7552638375e-12.5274889591+088.788449279494-1.77693466823e-8884418782+001.95284971187+4E82.8319869547a+0081.94129特征值-1.锡403982259++00对应的特征向量为：(-2.4848382252+085.091259892-01-1.482753484281+8-1.48S8532881e833998777+0阀-1.484361479621+088-1.铜058559854+08-1.48482423030+000-1.4398331697%+085.64354827408-H⁰2)特征值9.35897818e-谢对团的特征向量为：(1.935588251875+1.9附42405381-839.26681862717-谢9.227378151e-813592N?4+01+8981.06133463+-l8.416198235e-17.528673539e-4.86929持症值5.58489935Mle:对应的特证向为：(1.8564124521特性值9.e-001对应的特性向量为：(1.e+0001.e-0039.e-0019.e-001特性值6.e-001对应的特性向量为：(1.e+000-2.e-0016.e-0015.e-0016.e-0018.e-0017.e