消元法實(shí)驗(yàn)報(bào)告p9137

西京學(xué)院數(shù)學(xué)軟件實(shí)驗(yàn)任務(wù)書(shū)課程名稱數(shù)學(xué)軟件實(shí)驗(yàn)班級(jí)***學(xué)號(hào)***姓名***線性方程組直接三角分解法（Doolittle分解，Grout實(shí)驗(yàn)課題分解），平方根法（Cholesky分解，LDLT分解）熟習(xí)線性方程組直接三角分解法（Doolittle分解，實(shí)驗(yàn)?zāi)康腉rout分解），平方根法（Cholesky分解,LDLT分解）運(yùn)用Matlab/C/C++/Java/Maple/Mathematica等此中實(shí)驗(yàn)要求一種語(yǔ)言達(dá)成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)內(nèi)容成績(jī)教師實(shí)驗(yàn)報(bào)告實(shí)驗(yàn)名稱：Doolittle分解，Grout分解，平方根法Cholesky分解，LDLT分解實(shí)驗(yàn)?zāi)康模壕€性方程組直接三角分解法實(shí)驗(yàn)要求：求線性方程組的解試驗(yàn)流程：輸入所要求解的增廣矩陣用函數(shù)調(diào)用辦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程序此中兩個(gè)程序都是對(duì)矩陣的辦理；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)行增廣矩陣的辦理實(shí)驗(yàn)步驟：程序一：%SolveUpTrianglefunctionN=size(A);n=N(1);fori=n:-1:1if(1<n)

x=SolveUpTriangle(A,b)s=A(i,(i+1):n)*x((i+1):n,1);ealss=0;endx(i,1)=(b(i)-s)/A(i,i);end程序二：%SolveDownTrianglefunctionx=SloveDownTriang(A,b)N=size(A);n=N(1);fori=1:nif(i>1)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function[x丄,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);fork=2:nL(i,k)=A(i,k)-L(i,1:(k-1))*U(1:(k-1),k);endforj=(k+1):nU(k,j)=(A(k,j)丄(k,1:(k-1))*U(1:(k-1),j))/L(k,k);endendy=SolveDownTriangle(L,b);x=SolveUpTriangle(U,y);程序四：%Doolittle分解function[x丄,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);fork=2:nfori=k:nU(k,i)=A(k,i)-L(k,1:(k-1))*U(1:(k-1),i);endforj=(k+1):nL(j,k)=(A(j,k)-L(j,1:(k-1))*U(1:(k-1),k))/U(k,k);endendy=SolveDownTriangle(L,b);x=SolveUpTriangle(U,y);程序五：%Cholesky分解一function區(qū)L]=SymPosl(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);fork=2:nL(k,k)=sqrt(A(k,k)-L(k,1:(k-1))*transpose(L(k,1:(k-1))))fori=(k+1):nL(i,k)=(A(i,k)-L(i,i:(k-1))*transpose(L(k,1:(k-1))))/L(k,k);endendy=SolveDownTriangle(L,b);x=SolveUpTriangle(transpose(L),y);%Cholesky分解二functionN=size(A);n=N(1);L=eye(n,n);

[x,L,D]=SynPos2(A,b)d=zeros(n,1);fork=1:nd(k,1)=A(k,k)-L(k,1:(k-1))*L(k,1:(k-1))*d(1:(k-1),1);fori=(k+1):nL(i,k)=(A(i,k)-L(i,1:(k-1))*d(1:(k-1),1))/d(k,1);enden