Atiken加速一般迭代和牛顿迭代法

1、百度文库让每个人平等地捉升口我第二次上机实验报告实验=.用不动点迭代法求/(x) =x3-x-l = 0的根发散的迭代格式：xfc+1 = xj - 1,其中k=0. It 2收敛的迭代格式：Xfc+1 =其中k=0, X, 2X使用第二种格式迭代.且精度为10 M2)时，程序如下：转include iostreamz转include 转include znath. husing nazespace std:define h 0. 000000000001double f(double x) double fl = pow(x * 1, 1. 0 / 3):return fl:int main

2、() double xl, x2:int n=0:cout input first data:* h)(n+:xl = x2:cout setprecision(ll) x2 endl:x2 二 f(xl)：)cout result:*endl setprecision(H) x2 endl:cout n endl:return 0:输入初值为3的时候.结果如卜：对迭代格式使用Aitken加速观察其收敛散件质变化 对迭代恪式一使用Aitken加速.收敛对迭代恪式二使用Aitken加速.收敛速度变快程序如下：include include include define h 0.000000000

3、001 using namespace std;double f(double x) double fl = pow(x, 3)-1;return fl;int mainO double xO,xl, x2;int n = 0;cout please input the first number： xO;xl = f(x0);while (fabs(x0f(xO)h) n+;x2 = f (xl);xO = x2 - (x2 - xl)*(x2 - xl) / (x2 - 2 * xl + xO);xl = x2;cout setprecision(14) xO endl;cout resul

4、t: endlsetprecision(14) xO endl;coutnendl;return 0;对迭代格式二作Aikten加速迭代时，只需将函数f(x)替换为阪寸o初值为3的运行结果如卜：迭代格式一:DAv52015tnaLADebugtnolJ.exe- XplQasQ Input the st nunb： hJ2.96981627296SS 2.9388358583769 R2.9070103823506 Nz.874286873S8262.S406071706031 2.80S9072329943 2.7791163391703 2.7331S6148SS71 2.6949396D

5、2帖2 2.653696294236 2.6143376264527 2.S717216S8S963 2.527384423)74 2.48117010636 2.4320P生的27的 2.M2M的曲他722 2.320曲帖3262餌 2.273623362 务 Q 2.2248539384905 2.152095106908 2.8807848970181 2.W07143972745 1.9428641739338 1.8024015821270 1.7777135850576 1.6881023875648 1.59502306564341.5022731638921.418186697

6、3548 1.3567741254389 1.3292453527852 1.3248169440773 1.3247188652994 1.3247179572448 result:1.3247179572448迭代次数：34收敛于 1. 3247179572448迭代格式二：12迭代次数：3收敛丁： 1. 3247179572448实验二：./(%) = 3x-e=0,分析其有根区间： 尢=(p(x) = ln(x2) + ln(3) , 5ix0=3. 5,1,-0. 5 进行计算对比直接计算与Aitken加速的结果 .设计更多的X = p(x),采用更多的初值，重复的操作。1.因为f(

7、0)f(-l) 0且/(0)/(1) 0. /(3.7)/(3.8) -0.5时的Aitken加速迭代运行结果分别如卜:显然Aitken加速比一般迭代法收敛更加迅速，且当初值选择恰当时，收敛的值也在初值附近取丸o=4，3 5. E 0 5, -0. 5对 J (x)*3.5, 1, 0.一般迭代法：%0=4-e皿)=37-1, -35* 0.5 一1, 一3%o=3. 5 ChgO15M -OX3.322421440712 3.&41420110054 2.63W642136181 2.1012260&82643 |1.7011545877539 1.391S7S771W97 卜 13328?

8、如?429 l.ei8273166W22 . 066265415756 .93333333140883 .92821329574 .&14S7792520273 .9122263918161 ft.91117662904 机 913672835320? .01021676570533 .MB10276166845 e.915e8B495G61 札9丄(272因038为 .9100169595428 b 911165254146 卩91为妙289题5 .0ieGG417176W91 &8 70 5682513 p.91e77473632S |.91fe70S2DS729 机91哋766旳272

9、机 910756896167 机列*67579蛉397 .91&0757580068 .01006757404644 .91000757319475 .91000757280990 .910757268 机列做757255522 机91如6757251897 .0100757250248 .M0G0757249497 p.91e7S72491SC e.9ie75724$eei result： 0 勿删 7572493%0=1%o=0-5広衣55中讪.- O X6.741532419979C. 830700661851 6.87712774043028 O.KIS16W2755364 6.003

10、28114314911 .98695216255108 0.MSQ184 如 8330 b 9O9PS71811545 0.99972012176S66 b 9098?6?%71务2 C 90994886823428 C.OGOO8G4C23M O.OGWOS2S368205 6.9109019674025 0.910002215674 e.9100041207875 O.91O007044d979A 0 91W0733225够 d e. 91W0746317962 e. 0,3252273266 e.M0G0754gB5B62 6.01009756219193 e.9109075678836

11、4 0.9100757035&98 0.9100075715187? to.9107572W7J8 Q91倾75722879 6.9107572597)4 C.01000757244714 e.M0G0757246O7O 6.0100975724801 0.91D9075724S479 e.91e75724S&93 result：G 列沁”72阳？9%0二-0 56.45)62e.4ts*ie2ifriiR 4S99C*?R4A194S 6 45)62i6J?M48 0.4t0?D22M4M9t B.4S890220733776 e &期62267$82660.4&C22C7i2CC6.4SS

12、)6J26755M twit:8.3561866 306S6&5 8.WO1096d4K41 8.45511259079253 B.46 1866216114 e.4Sfi6S3867251 e.4W6i364SeJ110 8.4S94O0257242O 0.4S9O599a741O7 0.45fiQ614X2214S8 e.4S4?62463S17S4 0.43J622224W B.4S9O227787n9 8.4SS9O22G51C493 fl.4SS062268GS128 0.4S4?62267412e3 8 4砂6226756%】 0.4SS9O22O75WJ7 9.4S59O2207

13、5JW 0.4 沟622675166 8：4 如6226753703%o=3Jinput first data:卜3-0.128824258826021-6.541334293433 0.4444 241812089 |-0.a6J23172W7377L-O.4S79835514759r-G.4S801G71767456-G.4560555278864 fl-e.4S90289O227J J. 4*062,24573 的 0仪902380沁吨 *f 0.458962 2660827KO.45890220926464 04589622671443 Le.4SS0622076279J 卜9d矽62

14、267516刃-O.4SS9622674174 .45890220753589 -6.4S062267537a r5Ult:“S4SS0622675M6S i?AAitken加速法:妒1%o=3. 5%o=0-5%0二-0 5%0=一1%o=-3 D:vc20ntrial_3Dh.- XInput the first:OKlbP；AI-9.489S1399S898321-0.45897215800757 Nd.498962267938 |JlW8?i3175 5im73ie33WO10W75 701645砂73”782 &10O07724712 轲 和 7S7249026 1000757240

15、6?91O0e?S?248e72%0二0 5%o=-0 5溢出%o=l溢出%0=3溢出Aitken加速法:%o=3. 5f- O:vt2O15Uwl_5DebvgMnalJ. - X0.01018219511247 0.91GOe7S7ieei62 0.910797248871 result:0.91O997S7248871%o=0-5%o=-0 5j OWOWial.yvOebu - D Xease input th first rxnbor: .S.40211509241201 d如82253222# .4Sfi622683446S .4MM22675 砂58.4QG22M5 乂殆 OA.i2015Vybl_3Obu.-0.75034510515180