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add lecture 10

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rcc02007 committed Feb 20, 2017
1 parent de553ce commit 9b28df097f8b74a2aa329ba32e86ceef4a90840f
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{
"cells": [],
"metadata": {},
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}
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function [x,Aug] = GaussNaive(A,y)
% 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+1;
Aug = [A y];
% forward elimination
for k = 1:n-1
for i = k+1:n
factor = Aug(i,k)/Aug(k,k);
Aug(i,k:nb) = Aug(i,k:nb)-factor*Aug(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
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function [x,Aug,npivots] = GaussPivot(A,b)
% 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+1;
Aug=[A b];
npivots=0; % initially no pivots used
% forward elimination
for k = 1:n-1
% partial pivoting
[big,i]=max(abs(Aug(k:n,k)));
ipr=i+k-1;
if ipr~=k
npivots=npivots+1; % if the max is not the current index ipr, pivot count
Aug([k,ipr],:)=Aug([ipr,k],:);
end
for i = k+1:n
factor=Aug(i,k)/Aug(k,k);
Aug(i,k:nb)=Aug(i,k:nb)-factor*Aug(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
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function x = Tridiag(e,f,g,r)
% Tridiag: Tridiagonal equation solver banded system
% x = Tridiag(e,f,g,r): Tridiagonal system solver.
% input:
% e = subdiagonal vector
% f = diagonal vector
% g = superdiagonal vector
% r = right hand side vector
% output:
% x = solution vector
n=length(f);
% forward elimination
for k = 2:n
factor = e(k)/f(k-1);
f(k) = f(k) - factor*g(k-1);
r(k) = r(k) - factor*r(k-1);
end
% back substitution
x(n) = r(n)/f(n);
for k = n-1:-1:1
x(k) = (r(k)-g(k)*x(k+1))/f(k);
end
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\relax
\providecommand\hyper@newdestlabel[2]{}
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\global\let\hyper@last\relax
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\@writefile{toc}{\contentsline {section}{\numberline {1}Gauss Elimination}{1}{section.1}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.0.1}Solving sets of equations with matrix operations}{1}{subsubsection.1.0.1}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.1}Solving sets of equations systematically}{4}{subsubsection.1.1.1}}
\newlabel{solving-sets-of-equations-systematically}{{1.1.1}{4}{Solving sets of equations systematically}{subsubsection.1.1.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Springs-masses\relax }}{4}{figure.caption.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Automate Gauss Elimination}{6}{subsection.1.2}}
\newlabel{automate-gauss-elimination}{{1.2}{6}{Automate Gauss Elimination}{subsection.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Problem (Diagonal element is zero)}{6}{subsection.1.3}}
\newlabel{problem-diagonal-element-is-zero}{{1.3}{6}{Problem (Diagonal element is zero)}{subsection.1.3}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.3.1}Spring-Mass System again}{8}{subsubsection.1.3.1}}
\newlabel{spring-mass-system-again}{{1.3.1}{8}{Spring-Mass System again}{subsubsection.1.3.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Springs-masses\relax }}{9}{figure.caption.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}Tridiagonal matrix}{9}{subsection.1.4}}
\newlabel{tridiagonal-matrix}{{1.4}{9}{Tridiagonal matrix}{subsection.1.4}{}}
\gdef \LT@i {\LT@entry
{2}{67.64778pt}\LT@entry
{1}{261.39424pt}}
No changes.
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The top-level auxiliary file: lecture_10.aux
I found no \citation commands---while reading file lecture_10.aux
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(There were 3 error messages)

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