數(shù)值分析冪法課程設(shè)計(jì)用冪法求矩陣的最大特征值

1、課 程 設(shè) 計(jì) 報(bào) 告課程名稱 計(jì)算方法課程設(shè)計(jì) 課題名稱 用冪法求矩陣的最大特征值 專 業(yè) 班 級(jí) 學(xué) 號(hào) 姓 名 指導(dǎo)教師 目錄32. 問題的描述及算法設(shè)計(jì)43. 算法的流程圖44. 算法的理論依據(jù)及其推導(dǎo)45. 相關(guān)的數(shù)值結(jié)果86. 數(shù)值計(jì)算結(jié)果的分析91012一、設(shè)計(jì)內(nèi)容與設(shè)計(jì)要求1設(shè)計(jì)內(nèi)容： 對(duì)課程計(jì)算方法中的常見算法進(jìn)行綜合設(shè)計(jì)或應(yīng)用（具體課題題目見后面的供選題目）。2設(shè)計(jì)要求：l 課程設(shè)計(jì)報(bào)告正文內(nèi)容a. 問題的描述及算法設(shè)計(jì)；b. 算法的流程圖（要求畫出模塊圖）；c. 算法的理論依據(jù)及其推導(dǎo)；d. 相關(guān)的數(shù)值結(jié)果（通過程序調(diào)試)，；e. 數(shù)值計(jì)算結(jié)果的分析；f. 附件（所有程序

2、的原代碼，要求對(duì)程序?qū)懗霰匾淖⑨專 書寫格式a要求用A4紙打印成冊(cè)b正文格式：一級(jí)標(biāo)題用3號(hào)黑體,二級(jí)標(biāo)題用四號(hào)宋體加粗,正文用小四號(hào)宋體;行距為22。c正文的內(nèi)容:正文總字?jǐn)?shù)要求在3000字左右（不含程序原代碼）。d封面格式如下頁(yè)。l 考核方式指導(dǎo)老師負(fù)責(zé)驗(yàn)收程序的運(yùn)行結(jié)果，并結(jié)合學(xué)生的工作態(tài)度、實(shí)際動(dòng)手能力、創(chuàng)新精神和設(shè)計(jì)報(bào)告等進(jìn)行綜合考評(píng)，并按優(yōu)秀、良好、中等、及格和不及格五個(gè)等級(jí)給出每位同學(xué)的課程設(shè)計(jì)成績(jī)。具體考核標(biāo)準(zhǔn)包含以下幾個(gè)部分：a平時(shí)出勤 （占10%）b系統(tǒng)需求分析、功能設(shè)計(jì)、數(shù)據(jù)結(jié)構(gòu)設(shè)計(jì)及程序總體結(jié)構(gòu)合理與否（占10%）c程序能否完整、準(zhǔn)確地運(yùn)行，個(gè)人能否獨(dú)立、熟練地調(diào)

3、試程序（占40%）d設(shè)計(jì)報(bào)告（占30%）注意：不得抄襲他人的報(bào)告（或給他人抄襲），一旦發(fā)現(xiàn)，成績(jī)?yōu)榱惴?。e獨(dú)立完成情況（占10%）。l 課程驗(yàn)收要求a判定算法設(shè)計(jì)的合理性，運(yùn)行相關(guān)程序，獲得正確的數(shù)值結(jié)果。b回答有關(guān)問題。c提交課程設(shè)計(jì)報(bào)告。d提交軟盤（源程序、設(shè)計(jì)報(bào)告文檔）。e依內(nèi)容的創(chuàng)新程度，完善程序情況及對(duì)程序講解情況打分。3、進(jìn)度安排1、 班級(jí)： 信息與計(jì)算科學(xué)：0501、0502、05032、 主講教師：聶 存 云3、 輔導(dǎo)教師：聶 存 云、趙 釷 焱4、 時(shí)間安排：第 16 周 星期一 8時(shí)：00分16時(shí)：30分 星期三 8時(shí)：00分16時(shí)：30分 星期五 8時(shí)：00分16時(shí)：30

4、分 星期天 8時(shí)：00分11時(shí)：00分二、 問題的描述及算法設(shè)計(jì) 對(duì)于給定矩陣A用冪法求解矩陣A的最大特征值；本算法用于求矩陣按模最大的特征值及其相應(yīng)特征向量。程序執(zhí)行后，先通過鍵盤輸入矩陣、迭代初值向量、精度控制和迭代允許最大次數(shù)，程序即可給出每次迭代的次數(shù)和對(duì)應(yīng)的迭代特征值、特征向量及誤差序列，它們都按10位有效數(shù)輸出。其中最后輸出的結(jié)果即為所求的特征值和特征向量序列。如果迭代超出次還沒有求出滿足精度的根則輸出迭代超限提示，此時(shí)可以根據(jù)輸出序列判別收斂情況。三、 算法的描述；（1）輸入矩陣、初始向量，誤差；（2）；（3）計(jì)算；（4）；（5）；（6）如果,則顯示特征值和對(duì)應(yīng)的特征向量),終止

5、； （7）,轉(zhuǎn)（3）注：如上算法中的符號(hào)表示取向量中絕對(duì)值最大的分量。本算法使用了數(shù)據(jù)規(guī)范化處理技術(shù)以防止計(jì)算過程中出現(xiàn)益出錯(cuò)誤。四、 算法的理論依據(jù)及其推導(dǎo)； 冪法是通過求矩陣特征向量來求出特征值的一種迭代法.其基本思想是:若我們求某個(gè)n階方陣A的特征值和特征向量,先任取一個(gè)初始向量X(0),構(gòu)造如下序列: X(0) ,X(1) =AX(0) ,X(2) =AX(1) , X(K) =AX(K+1) , 當(dāng)k增大時(shí),序列的收斂情況與絕對(duì)值最大的特征值有密切關(guān)系,分析這一序列的極限,即可求出按模最大的特征值和特征向量. 假定矩陣A有n個(gè)線性無關(guān)的特征向量.n個(gè)特征值按模由大到小排列: 1=2=

6、n 其相應(yīng)的特征向量為: V1 ,V2 , ,Vn 它們構(gòu)成n維空間的一組基.任取的初始向量X(0)由它們的線性組合給出 X(0)=a1V1+a2V2+anVn 由此知,構(gòu)造的向量序列有 X(k) =AX(k-1) = A2X(k-2) =AkX(0) = a11kV1+a2 2kV2+annkVn 下面按模最大特征值1是單根的情況討論: 由此公式(5)可寫成 X(k) = 1k (a1V1+a2 (2/1)kV2+an(n/1)kVn ) 若a10，由于|i/1 |1 (i2),故k充分大時(shí)， X(k) = 1k (a1V1+k) 其中k為一可以忽略的小量，這說明X(k)與特征向量V1相差一

7、個(gè)常數(shù)因子，即使a1=0，由于計(jì)算過程的舍入誤差，必將引入在方向上的微小分量，這一分量隨著迭代過程的進(jìn)展而逐漸成為主導(dǎo)，其收斂情況最終也將與相同。特征值按下屬方法求得： 1 Xj(k+1)/ Xj(k) 其中Xj(k+1)， Xj(k)分別為X(k+1)，X(k)的第j各分量。 實(shí)際計(jì)算時(shí)，為了避免計(jì)算過程中出現(xiàn)絕對(duì)值過大或過小的數(shù)參加運(yùn)算，通常在每步迭代時(shí)，將向量“歸一化”即用的按模最大的分量 max |Xj(k)| 1jn去除X(k)的各個(gè)分量,得到歸一化的向量Y(k),并令X(k+1) = AY(k)由此得到下列選代公式 : Y(k) = X(k)/ X(k) X(k+1) = AY(k

8、) k=0,1,2, 當(dāng)k充分大時(shí),或當(dāng) X(k)- X(k+1)時(shí), Y(k)V1 max |Xj(k)| 1 1jn五、 相關(guān)的數(shù)值結(jié)果（通過程序調(diào)試)，； 六、 數(shù)值計(jì)算結(jié)果的分析；對(duì)于同一個(gè)矩陣，給定不同的處值及精度計(jì)算出的結(jié)果如下七、 附件 #include #include#include#define eps 1e-6int main() float Maxline(float* p); float Matrix1616 = 0 , x16 = 0 , Init16 = 0 , fore16 = 0; float MaxCV = 0 , eps2 = 100; int i = 0

9、 , j = 0 , t = 0 , col = 0; printf(The Matrixs col is : ); scanf(%d , &col); printf(The Matrix is n); for(i = 0 ; i col ; i +) for(j = 0 ; j col ; j +) scanf(%f , &Matrixij); printf(The Init is n); for(i = 0 ; i col ; i +) scanf(%f , &Initi); for(j = 0 ; j 10 ; j +) MaxCV = Maxline(Init); for(i = 0

10、; i col ; i +) xi = (Initi / MaxCV); for(i = 0 ; i col ; i +) printf(%.4ft , Initi); printf(t%.4ftt , MaxCV); for(i = 0 ; i col ; i +) printf(%.4ft , xi); for(i = 0 ; i col ; i +) forei = Initi; Initi = 0; for(t = 0 ; t col ; t +) Initi += (Matrixit * xt); if(fabs(Initi - forei) eps2) eps2 = fabs(In

11、iti - forei); printf(n); if(eps2 eps) break; getch();float Maxline(float* p) float max = 0; int i = 0; for(i = 0 ; *(p + i) != 0 ; i +) if(max *(p + i) max = *(p + i); return max;八，總結(jié) 在這次的編程練習(xí)中我學(xué)到了很多東西，在多次的c編程中我學(xué)會(huì)了種種不同的有效算法，并且更熟練的掌握了一些編程技巧。在多次的編寫，調(diào)試和運(yùn)行程序中我更加深刻的了解了一些算法的優(yōu)越性和一些問題。這是我在以后的編程過程中更加深刻的思考和努力

12、的學(xué)習(xí)。數(shù)理系課程設(shè)計(jì)評(píng)分表課程名稱： 項(xiàng) 目評(píng) 價(jià)設(shè)計(jì)方案的合理性與創(chuàng)造性設(shè)計(jì)與調(diào)試結(jié)果設(shè)計(jì)說明書的質(zhì)量答辯陳述與回答問題情況課程設(shè)計(jì)周表現(xiàn)情況綜合成績(jī) 教師簽名： 日 期： 內(nèi)部資料僅供參考9JWKffwvG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ!djs#XuyUP2kNXpRWXmA&UE9aQGn8GK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxG89AmUE9aQGn8xp$R#͑GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zV

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25、z849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqvadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2z

26、Vkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRr

27、WwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vS

28、TT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89Amv$UE9wEwZ#QcUE%&

29、qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5u

30、xY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9C

31、pbK!zn%MadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*adNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$v

32、STT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849

33、GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89A

34、mYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTX

35、Rm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9Cp

36、bK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$

37、U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjq

38、v$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4

39、NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnG

40、K8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuW

41、FA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuW

42、FA5uxY7JnD6YWRrWwcvR9CpbK!zn%MzadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9w

43、EwZ#QcadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum

44、&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*

45、3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*

46、3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpE

47、h5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6

48、X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn

49、%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK

50、8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqvUE%&qYpEh5pDx2zVkum&gTXR

51、m6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWF