北航数值分析作业第二题

拟上三角化后的矩阵为： 第一、二、三列 -8.827516758830e-001 -9.933136491826e-002 -1.103349285994e+000 -2.347878362416e+000 2.372370104937e+000 1.819290822208e+000 -1.055685482407e-016 1.728274599968e+000 -1.171467642785e+000 -5.393383812774e-017 -3.165873865181e-017 -1.291669534130e+000 1.533464996622e-017 5.963321406181e-017 -3.273062155360e-017 1.300562737229e-016 -3.097060010889e-017 8.556127565867e-017 1.610216724767e-016 -2.211571837369e-016 -3.925484904011e-017 1.368550186199e-016 7.151513190805e-017 -8.672615311204e-017 -2.780851300718e-017 -6.708630788363e-017 8.476127173939e-017 -2.124604440055e-017 -1.707979758930e-016 -2.798942287067e-017 第四、五、六列 -7.600443585637e-001 1.549101079914e-001 -1.946591862872e+000 3.237804101546e-001 2.205798440320e-001 2.102692662546e+000 -1.243839262699e+000 -6.399758341743e-001 -2.002833079037e+000 -1.111603513396e+000 1.171346824096e+000 -1.307356030021e+000 1.560126298527e+000 8.125049397515e-001 4.421756832923e-001 0.000000000000e+000 -7.707773755194e-001 -1.583051425742e+000 0.000000000000e+000 0.000000000000e+000 -7.463453456938e-001 0.000000000000e+000 0.000000000000e+000 -1.072074718358e-016 0.000000000000e+000 0.000000000000e+000 -4.879774287475e-017 0.000000000000e+000 0.000000000000e+000 4.153758325241e-017 第七、八、九列 -8.782436382927e-002 -9.255889387184e-001 6.032599440534e-001 1.816138086098e-001 1.278839089990e+000 -6.380578124405e-001 2.924947206124e-001 -6.412830068395e-001 9.783997621285e-002 1.803699177750e-001 -4.246385358369e-001 7.988955239304e-002 -3.588616128137e-002 4.691742313671e-001 -2.736595050092e-001 -3.042843176799e-001 2.528712446035e-001 -6.709925401449e-001 -2.708365157019e-002 -9.486521893682e-001 1.195871081495e-001 -7.701801374364e-001 -4.697623990618e-001 4.988259468008e-001 1.854829286220e-016 7.013167092107e-001 1.582180688475e-001 1.222621691887e-016 0.000000000000e+000 4.843807602783e-001 第十列 1.518860956469e-001 -4.154075603804e-001 2.557763574160e-001 1.608819928069e-001 -7.359334657750e-002 2.544619929082e-001 1.929265617952e-002 1.137691603776e-001 3.862594614233e-001 3.992777995177e-001 进行QR分解后得到的矩阵为： 第一、二、三列 3.383039617436e+000 8.948776653934e-001 -8.956760707771e-001 2.996220399126e-020 -2.118477462415e+000 -2.361527908197e+000 -1.166749166266e-025 3.555130770734e-001 -2.528514958008e+000 1.291629815233e-028 -7.031035206701e-024 1.023011470128e-016 -1.019096126668e-032 -9.466330862652e-030 -8.370509664169e-023 2.902053379130e-032 5.731876308595e-030 -4.210292585179e-029 1.541551074536e-032 3.166101416224e-030 -2.336513400496e-029 -1.090506818587e-031 -8.470763687191e-031 4.273061155532e-030 1.258099647470e-030 3.634355341129e-029 -1.441569320750e-028 6.462444347901e-032 -9.189135613071e-031 2.219698065431e-030 第四、五、六列 -8.465132300413e-002 2.612678569484e-001 1.610395626348e+000 3.455608690435e-002 -4.736643858907e-002 1.816396880193e+000 6.375263127570e-001 2.023815197668e-002 1.838634773491e+000 1.577548568535e+000 1.395961638848e-002 -6.971939617089e-001 -2.505059418817e-006 -1.484039833681e+000 -1.005290438434e-001 -6.521059057906e-026 3.831240511625e-021 -6.948731242870e-001 -3.574572100727e-026 -4.400387990121e-025 1.788254275759e-001 -1.320810060830e-027 -1.369873042080e-026 -1.033975765691e-025 7.004776349698e-028 -4.980853436016e-028 -4.605117003418e-026 1.394783029422e-029 7.455288336328e-030 6.078123213096e-028 第七、八、九列 -1.022617600648e+000 9.371886210517e-002 -1.002578700819e+000 -2.319028623993e-001 -1.435516012783e-001 -6.537076947736e-001 1.868711335362e-001 -2.932577853277e-001 1.987065844236e+000 1.555704836928e-001 8.405054265524e-003 -8.154391705301e-002 4.249917720387e-002 2.623603124719e-002 1.040075636772e-001 -5.289222734276e-001 2.679156722088e-001 -5.962368505136e-001 -1.266188788293e+000 4.715000043040e-002 2.904780036862e-001 -1.246416426510e-020 9.355889078188e-001 1.877411051006e-001 -3.618844445919e-025 -4.538007978554e-014 6.360511809675e-001 4.281740120959e-027 -1.724505947937e-024 2.457611070758e-005 第十列 -4.086260812331e-001 3.227152127670e-002 1.004631189782e+000 -1.086119035375e-001 -1.180720843088e-001 -4.911592278219e-001 -3.570390800483e-002 1.360256519299e-001 2.737034413476e-001 5.651649654208e-002 已得到所有特征值如下： 1: 3.383039617436e+000 2: -2.323496210212e+000-j8.930405177200e-001 3: -2.323496210212e+000+j8.930405177200e-001 4: -1.484039822259e+000 5: 1.577548557113e+000 6: -9.805309562902e-001-j1.139489127430e-001 7: -9.805309562902e-001+j1.139489127430e-001 8: 9.355889078188e-001 9: 5.650488993501e-002 10: 6.360627875745e-001 对应于特征值3.383039617436e+000的特征向量为： -1.052215734361e-001 -2.183641973272e-001 -4.730178777759e-001 -2.608874788703e-001 -3.058056251403e-001 -2.583797832214e-001 8.733793639504e-002 4.054540338526e-001 5.090131137202e-001 2.409250445621e-001 对应于特征值-1.484039822259e+000的特征向量为： 5.601181168002e-001 -7.793415087696e-001 -1.337801148565e-002 2.774092878906e-001 -3.005575882933e-003 2.534834089619e-003 2.062848490886e-002 1.101348291069e-002 1.224861665247e-002 -3.236209304084e-002 对应于特征值1.577548557113e+000的特征向量为： -6.249625599170e-002 1.120900451498e-002 2.496667051788e-001 1.313644861499e-001 3.835412561201e-001 -8.159443103525e-001 1.245603520674e-001 6.835610547252e-002 -2.705874017774e-001 -1.005191081460e-001 对应于特征值9.355889078188e-001的特征向量为： -8.056515482686e-002 -4.611134688033e-002 1.502437919757e-002 4.812083461841e-002 3.536338920690e-001 -2.089190778112e-001 1.557459663954e-001 -8.196704272714e-001 3.509825128186e-001 -2.885138527827e-002 对应于特征值5.650488993501e-002的特征向量为： 2.090175185816e-001 2.000637966850e-001 -3.891760618167e-001 2.779391187066e-002 3.932365479058e-001 1.247038109522e-001 -6.448109395584e-001 3.027798531084e-001 2.910952633143e-001 -4.094365558116e-002 对应于特征值6.360627875745e-001的特征向量为： 1.070374683972e-001 7.123455832557e-002 3.902379171386e-001 -4.466555137564e-002 -7.190347442747e-001 1.758156884395e-001 -2.265379615437e-001 3.768861505018e-001 2.956254085051e-001 2.255779725592e-002