消元法實(shí)驗(yàn)報(bào)告

1、西京學(xué)院數(shù)學(xué)軟件實(shí)驗(yàn)任務(wù)書線性方程組直接三角分解法（Doolittle分解，Grout分解），平方根法（Cholesky分解，LDLT分解）熟悉線性方程組直接三角分解法（Doolittle分解,Grout分解），平方根法（Cholesky分解，LDLT分解）運(yùn)用Matlab/C/C+/Java/Maple/Mathematica等其中線性方程組直接三角分解法（Doolittle分解，Grout分解）線性方程組平方根法（Cholesky分解，LDLT分解）實(shí)驗(yàn)報(bào)告Doolittle分解，Grout分解，平方根法Cholesky分解，LDLT分解課程名稱數(shù)學(xué)軟件實(shí)驗(yàn)班級(jí)*學(xué)號(hào)姓名實(shí)驗(yàn)內(nèi)容成績(jī)教師實(shí)

2、驗(yàn)?zāi)康? 線性方程組直接三角分解法實(shí)驗(yàn)要求: 求線性方程組的解實(shí)驗(yàn)課題實(shí)驗(yàn)?zāi)康膶?shí)驗(yàn)要求一種語言完成實(shí)驗(yàn)名稱:試驗(yàn)流程:輸入所要求解的增廣矩陣用函數(shù)調(diào)用處理矩陣輸出方程組的解實(shí)驗(yàn)工具：matlab軟件實(shí)驗(yàn)原理：用matlab軟件先編譯SolveDownTriangle和SolveUpTriangle程序其中兩個(gè)程序都是對(duì)矩陣的處理;Doolittle分解，Grout分解，平方根法Cholesky分解，LDLT分解都調(diào)用他們兩個(gè)函數(shù)進(jìn)行增廣矩陣的處理實(shí)驗(yàn)步驟:程序一：%SolveUpTrianglefun cti onx=Solve Up Tria ngle(A,b)N=size(A);n=N(1

3、);for i=n:-1:1if (11) s=A(i,1:(i-1)*x(1:(i-1),1);elses=0;endx(i,1)=(b(i)-s)/A(i,i);end程序三:% Grout分解fun ctionx,L,U=Crout(A,b)N=size(A); n=N(1); L=zeros (n,n);U=eye( n,n);L(1: n,1)=A(1: n,1)U(1,1: n) =A(1,1: n)/L(1,1);for k=2: nL(i,k)=A(i,k)-L(i,1:(k-1)*U(1:(k-1),k);end for j=(k+1): nU(k,j)=(A(k,j)-L(

4、k,1:(k-1)*U(1:(k-1),j)/L(k,k);end end y=SolveDow nTria ngle(L,b); x=SolveU pTria ngle(U,y);程序四:% Doolittle分解fun ctionx,L,U=Doolittle(A,b)N=size(A);n=size(A);L=eye( n,n);U=zeros( n,n);U(1,1: n) =A(1,1: n);L(1: n,1)=A(1: n,1)/U(1,1); for k=2: nfor i=k: nU(k,i)=A(k,i)-L(k,1:(k-1)*U(1:(k-1),i);endfor j=

5、(k+1):nL(j,k)=(A(j,k)-L(j,1:(k-1)*U(1:(k-1),k)/U(k,k);end end y=SolveDow nTria ngle(L,b); x=SolveU pTria ngle(U,y);程序五:% Cholesky分解一fun ctionx,L=Sy mP osl (A,b)N=size(A);n=N(1);L(1,1)=sqrt(A(1,1);L(2:n ,1)=A(2: n,1)/L(1,1);for k=2: nL(k,k)=sqrt(A(k,k)-L(k,1:(k-1)*tra nsp ose(L(k,1:(k-1)for i=(k+1):n

6、L(i,k)=(A(i,k)-L(i,i:(k-1)*tra nsp ose(L(k,1:(k-1)/L(k,k);end end y=SolveDow nTria ngle(L,b); x=Solve Up Tria ngle(tra nspose(L),y);% Cholesky分解二fun ctionx,L,D=Sy nP os2 (A,b)N=size(A);n=N(1);L=eye( n,n);d=zeros (n ,1);for k=1: nd(k,1)=A(k,k)-L(k,1:(k-1)*L(k,1:(k-1)*d(1:(k-1),1); for i=(k+1):nL(i,k)=(A(i,k)-L(i,1:(k-1)*d(1:(k-1),1)/d(k,1);end endD=diag(d);y=So