1、實驗三 解線性方程組的迭代法(1)雅可比迭代法1、實驗程序實現雅可比迭代法的MATLAB數文件agui_jacobi.m2 34 -5 - 6 -7 - 8 - 9 -10 - 11 -12 - 13 -14 - 15 -16 - 17 - IS - 19 - 20 - 21 -22 -23function z = agui_jacobi (a, b)為系數矩陣, b為右端向量,區口為初始向量(默認為零向量)加為精度默認為154)，W為最大迭代次數(默認】?？?1笈為返回解向量 n=lengthCb) tN=1DO;e=1e-4;xO=zeros (n3 1) hx=xO;x0=x+2*e;k

2、=0;d= di ag (diag (a);l=-tril(a,-10 hu二一triu(a, 1);while norm (xO_Xj inf) >e4k<Nk=k+l;xO=x;x=inv(d) * (1+u) *x+inv(d) *b;kdisp )endif k=N WARNING C已達最大迭代次數;end24在MATLAB令窗口輸入及實驗結果和操作界面J Command WindowTo get startedj select MATLAB H.lp or Dem口理 from the Help menu.The element type "naneA mus

3、t be terminated by the matching end-tag *</name”.Could not parse the file: c:natlab7toolboxccslinkccslinkinfo.xml» a=4 -1 0 -1 0 0；-l 4 -1 0 -1 。;0 -1 4 -1 0 -1,-1 0 -1 4 -1 0.0 -1 0 -1 4 -1;D 0 -1 0 -1 44-10-10-14-10-10T4-10-10-14-10T0-1400-10-10070-14» b=0;5；-2；5-2；6b =05-25-26»

4、K=agui_jacobiC&b)k -1L 2500-0,5000 L500001,2500-0.50000. 62501.00000.50001.00000.50001. 25000.50001.65630.31251.65630.31251.7500k =40.8281k =50. 7656k =61.53130.76561. 83980. 67971. 53130.76561.65631. 83980.67971. 88280.89061.92530.85061.92530.85061.9453k =80.9626k =90. 94901. 89790.94901. 89790

5、.94901.92531. 96510.93031. 96510.93031.974510U. 982611l.952qU.9,621.9524U.9,621.9651120.99191.97780.98891.97780.98891.9837k =130.98891.99240. 98481. 99240.98481.9944140. 9962150. 9948161.98961.99650. 99480.99291.98961.99650. 99480.99291.99241. 9974170. 99761. 99830.99671. 99830.99671. 9988180.99921.

6、99770.99891. 99770.99891. 9983190.99891.99920.99851.99920.99851.9994200.99961.99890.99951.99890.99951.999221220.99981.99950.99981. 99950.99981.9996k =230. 99981.99980.99971. 99980.99971. 9999240. 99991.99980.99991.99980.99991. 9998250.99991.99990.99981.99990.99981.999926O+9S9S 2.00000.99992.00000. 9

7、9992* 口叩口0.9999 2. 0000 0.99992. 0000 0. 9999 2. 0000(2)高斯-賽德爾迭代法1、實驗程序實現高斯-賽德爾迭代法的MATLA函數文件agui_GS.mRft FiM IN J Tpmr;Qarinjir-qa2 M由寄吐*距b由E*向*- xl力M由何I監i匕電代表酸d力延回即4 - h=«h£rhft). 3 - R=IW.4 - «=1I: F - Riarxglb.3 " X"iD.X13Bz+2"!i.Tlfirnlfi2"un-r-iL 如la IK*EHljE【

8、F Ulf XU<H k=k+L.Nt=E.K=T北(4-411 STft+n，. ff t IcridxiplM，H! k«H /Uai!*/EE：士華亡MV ) «il23456789101112131415161718192021222324function x = agui_GS(a,b)為系數矩陣，b為右端向量, 乂口為初始向量(默認為零向量)灰為精度(默認為1總7)，N為最大迭代次數默認為1口。)為返回解向量- n=length(b);- N=100,- e=le-4;- xO=zeros (n3 1);- x=x0;- x0=x+2*e；- k=0;-

9、al=tril(a);- a2=inv(al);- while norm(kO-Zj inf)>eftk<N- k=k+1；- xO=z;- x-a2*(a-al) *x0+a2*b;- forjuatlong- k- disp(£)- end- if k=N WARNING C已達最大迭代次數Q- end在MATLAB令窗口輸入及實驗結果和操作界面» a=4-1 0 -10 0;-l4-10-10;0 -14-10 -1;-1 0-14-1 0;0 -10-14 -l;0 0-10-1 4a =4-10-100-14-10-100-14-10-1-10-14-

10、100-10-14-100-10-14» b=0;5;-2;5;-2; 6b =05-25-26» x=agui_GS (a, b)k =101.25000000000000 -0.187500000000001.203125000000000.113281250000001.481445312500000.61328125000000k =30.73643493652344k =40.87300521135330k =50.93943285173737k =60.970875459909621.384765625000001.715141296386721.8638888

11、89551161.934219151618891.968361701603950.517333984375000.764286994934080.884101506322620.944355651925430.973321806562521.560974121093751.776879549026491.893842517398301.949282688019591.975603240263230.606796264648440.818263351917270.913342248415570.958215694580760.979901944623431.781032562255861.895

12、637586712841.949360938684551.975642836626551.988305937796490.98599123546679k =80.99326789987023k =90.99676495834023k =100.99844528982311k =110.999252825423461.984803746663191.992697628842581.996490403508261.998313328403621.999189418716950.987178231180730.993836533883830.997037942987460.9985765225339

13、10.999315901092071.988267852817741.994362204518351.997290755784171.998697973290231.999374263356490.990344384319350.995360121808990.997770080803910.998928326910420.999484973608631.994380653875021.997299163923211.998702005947841.999376212361081.99970021867517k =12File Edit Debug Desktop Wndcw Help0.99

14、9640920518361.999610448804760.999671232709111.933599281709020.999762487297241.99985533000159130. 99982M32628451.999812788158701.993855479973250. 99988104953338L999930732375180.999917067032991.99991002913342D.999924067870461.999930546109210.999942834404451.99995572556873x -0.999�.999924067870461.999930546109210.999942834404451.99996672556873結果分析:從上面的雅可比迭代法和高斯一賽德爾迭代法這兩種方法所得的實驗結果可知，對于同樣的矩陣：a =4-10-100-14-10-100-14-10-1