高斯消去法解線性方程的Matlab程序

1151091楊晨輝高斯消去法解線性方程的 Matlab程序方法一：functionx=gauss(A,b)n=length(b);fork=1:n-1ifA(k,k)==0fprintf( 'Error:the%dthpivotelementequaltozero!\n' ,k);return;endindex=[k+1:n];m=-A(index,k)/A(k,k);A(index,index)=A(index,index)+m*A(k,index);b(index)=b(index)+m*b(k);endx=zeros(n,1);x(n)=b(n)/A(n,n);fori=n-1:-1:1x(i)=(b(i)-A(i,[i+1:n])*x([i+1:n]))/A(i,i);end運(yùn)行結(jié)果：>>A=[11.3551.42; 33.50.221; 0.522.13; 0.30.1-0.552];>>b=[2.00,1.00,0.55,3.00]'b=2.00001.00000.55003.0000>>gauss(A,b)ans=2.5225-2.23130.01771.2381方法二：矩陣求逆：function[B]=qiuni(A)%UNTITLEDSummaryofthisfunctiongoeshere%Detailedexplanationgoesheren=numel(A);r=rank(A);B=eye(r);ifn==rA2fork=1:rfori=1:rforj=1:rii=i-1;jj=j-1;ifii==0&&jj==0;ii=r;jj=r;B(ii,jj)=1/A(1,1);elseifii==0&&jj~=0;ii=r;B(ii,jj)=-A(1,j)/A(1,1);elseifjj==0&&ii~=0;jj=r;B(ii,jj)=A(i,1)/A(1,1);elseB(ii,jj)=A(i,j)-A(i,1)*A(1,j)/A(1,1);endendendA=B;B=eye(r);endB=A;elsemsgbox('矩陣不可逆','message','warn');endend當(dāng)方程不可逆時(shí):第二種：function[B]=lyxqinv(A)%UNTITLEDSummaryofthisfunctiongoeshere%Detailedexplanationgoesheren=numel(A);r=rank(A);B=eye(r);ifn==rA2E=eye(r);A=[AE];fork=1:(r-1)fori=(k+1):rforj=(k+1):2*rA(i,j)=A(i,j)-A(i,k)*A(k,j)/A(k,k)；endj=k；A(i,j)=A(i,j)-A(i,k)*A(k,j)/A(k,k)；endendfork=2:rfori=1:(k-1)forj=(k+1):2*rA(i,j)=A(i,j)-A(i,k)*A(k,j)/A(k,k);endj=k；A(i,j)=A(i,j)-A(i,k)*A(k,j)/A(k,k);endendfori=1:rforj=1:2*rB(i,j)=A(i,j)/A(i,i);endendB=B(:,(r+1):2*r);elsemsgbox('矩陣不可逆‘，’message','warn');endend隅XsIKA!41I?UCW.l心gj■:■堂“AC*MTih?24irwr*■ Ph1AlfMq-fli Mflt-^OM-^217I5CB■]lyrqmsn M-lMc-2014^-321S1:63^■|trt?H1> Nfit3tl*aiTWM1■"rErWwiiwMep?C口ifljri事尸了p翼jlG她!h>一強(qiáng)413.??AMITt,23t1]>[1?101KF*掛圖i)2,4S(3JIF配23B小6I如V?[專4J2；4￡ft3；311S；f.3B I薩0113,4 >IFt.Si911 IId■■Eftid-^vlac-i41」一h*4ri-QkUthaHi>L*ILSIM?a.2E憫，awna*TNf3?>隼MF>-a.na^-aMi，du[lil#KDLMab盤CLnA?Cl11-11.1-I-14,11 40二[-112.4F93:11IT￥;?1nimqE■心■IV411m111lIKit3I1J.CMMIiraiFiaF區(qū).力1Lt-fr-2FMiJfrfHE1rf5,1II>:5,3B11EVMUMV^方程求解:functionX=jie(A,b);[m,n]=size(A);B=[A,b];RA=rank(A);RB=rank(B);formatratifRA==RB&RA==n峪梅方程有唯一解X=A\b;elseifRA==RB&RA<n喈U斷方程有無窮解X=A\b 漁特解C=null(A,'R'); 漁AX=0B勺基礎(chǔ)解系elseX='方程無解’； 喈U斷方程無解endend工& a$II】點(diǎn)■梅崖丁;工|才|[?口|麗，>K 知￡&L]?^[]E-l9A)I|].|ri￡HMI>I0.?口卓同I土5!jgl4MI工& a$II】點(diǎn)■梅崖丁;工|才|[?口|麗，>K 知￡&L]?^[]E-l9A)I|].|ri￡HMI>I0.?口卓同I土5!jgl4MI>ItL吐同It3L?2C1)LTEJ站值i13,?2tLfS,JMl,I1L43?11IrV.t11*但A展iJ2.42?3.1Lr5,J仙?出巾JT5-1,2LSjlit出帖■BE4 1 S,? A i li i. f t：t?值i 1 !.< 2 A 3.1 L r S：2上帆t 3 2.4 2 ? 3.1 L f fl.JftUiNH疣iA20EM0上圖的方程有兩個(gè)，第一個(gè)有解，顯示結(jié)果；第二個(gè)無解，顯示 方程無解當(dāng)方程有無窮解時(shí)，顯示其特解?OKW2H2a?(tWI/t-(QF”「UM"儕，ox“HlMEdI即ZPZC-11-Cl-C2-l|=T《fl41 93