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added lecture 11

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rcc02007 committed Feb 23, 2017
1 parent 35dbdeb commit 46f626edf1d24a7dc9a189eb6c4ba024123f8242
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function [L, U] = LU_naive(A)
% GaussNaive: naive Gauss elimination
% x = GaussNaive(A,b): Gauss elimination without pivoting.
% input:
% A = coefficient matrix
% y = right hand side vector
% output:
% x = solution vector
[m,n] = size(A);
if m~=n, error('Matrix A must be square'); end
nb = n;
L=diag(ones(n,1));
U=A;
% forward elimination
for k = 1:n-1
for i = k+1:n
fik = U(i,k)/U(k,k);
L(i,k)=fik;
U(i,k:nb) = U(i,k:nb)-fik*U(k,k:nb);
end
end
%% back substitution
%x = zeros(n,1);
%x(n) = Aug(n,nb)/Aug(n,n);
%for i = n-1:-1:1
% x(i) = (Aug(i,nb)-Aug(i,i+1:n)*x(i+1:n))/Aug(i,i);
%end
@@ -0,0 +1,36 @@
function [L,U,P] = LU_pivot(A)
% GaussPivot: Gauss elimination pivoting
% x = GaussPivot(A,b): Gauss elimination with pivoting.
% input:
% A = coefficient matrix
% b = right hand side vector
% output:
% x = solution vector
[m,n]=size(A);
if m~=n, error('Matrix A must be square'); end
nb = n;
L=diag(ones(n,1));
U=A;
P=diag(ones(n,1));
% forward elimination
for k = 1:n-1
% partial pivoting
[big,i]=max(abs(U(k:n,k)));
ipr=i+k-1;
if ipr~=k
P([k,ipr],:)=P([ipr,k],:); % if the max is not the current index ipr, pivot count
%L([k,ipr],:)=L([ipr,k],:);
%U([k,ipr],:)=U([ipr,k],:);
end
for i = k+1:n
fik=U(i,k)/U(k,k);
L(i,k)=fik;
U(i,k:nb)=U(i,k:nb)-fik*U(k,k:nb);
end
end
% back substitution
%x=zeros(n,1);
%x(n)=Aug(n,nb)/Aug(n,n);
%for i = n-1:-1:1
% x(i)=(Aug(i,nb)-Aug(i,i+1:n)*x(i+1:n))/Aug(i,i);
%end
@@ -0,0 +1,28 @@
\relax
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
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\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\providecommand \oddpage@label [2]{}
\@writefile{toc}{\contentsline {section}{\numberline {1}LU Decomposition}{1}{section.1}}
\newlabel{lu-decomposition}{{1}{1}{LU Decomposition}{section.1}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.0.1}efficient storage of matrices for solutions}{1}{subsubsection.1.0.1}}
\newlabel{efficient-storage-of-matrices-for-solutions}{{1.0.1}{1}{efficient storage of matrices for solutions}{subsubsection.1.0.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Pivoting for LU factorization}{2}{subsection.1.1}}
\newlabel{pivoting-for-lu-factorization}{{1.1}{2}{Pivoting for LU factorization}{subsection.1.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Springs-masses\relax }}{5}{figure.caption.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Cholesky Factorization}{6}{subsection.1.2}}
\newlabel{cholesky-factorization}{{1.2}{6}{Cholesky Factorization}{subsection.1.2}{}}
No changes.
@@ -0,0 +1,48 @@
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(There were 3 error messages)

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