Project 3 Solutions

Project 3 Solutions - Project 3 Group name: Unknowns Group...

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Unformatted text preview: Project 3 Group name: Unknowns Group members: Annon, Sofia, Hristian, Divya 1. Matlab code: function [L,U]=mylu(A) m=size(A,1); U=A; L=eye(m); for i=1:m-1 for j=i+1:m a=-U(j,i)/U(i,i); U(j,:)=a*U(i,:)+U(j,:); L(j,i)=-a; end end >> A=rand(5) A = 0.2028 0.0153 0.4186 0.8381 0.5028 0.1987 0.7468 0.8462 0.0196 0.7095 0.6038 0.4451 0.5252 0.6813 0.4289 0.2722 0.9318 0.2026 0.3795 0.3046 0.1988 0.4660 0.6721 0.8318 0.1897 >> [L,U]=mylu(A) L = 1.0000 0 0 0 0 0.9801 1.0000 0 0 0 2.9778 0.5461 1.0000 0 0 1.3424 1.2453 0.9402 1.0000 0 0.9805 0.6163 0.0073 0.3323 1.0000 U = 0.2028 0.0153 0.4186 0.8381 0.5028 0 0.7318 0.4359 -0.8018 0.2167 0 0 -0.9595 -1.3767 -1.1867 0 0.0000 0 1.5472 0.4756 0 0.0000 0 0 -0.5863 >> A-L*U ans = 1.0e-015 * 0 0 0 0 0 0 0 0 -0.0486 0 0 0 0 0 0.3331 0 0 -0.0278 0.1110 0 0 0 0 0.1110 -0.0278 We can see that L is lower triangular and that U is upper triangular and that L*U does equal A because the exponent is extremely small. >> A=magic(5) A = 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 >> [L,U]=mylu(A) L = 1.0000 0 0 0 0 1.3529 1.0000 0 0 0 0.2353 -0.0128 1.0000 0 0 0.5882 0.0771 1.4003 1.0000 0 0.6471 -0.0899 1.9366 4.0578 1.0000 U = 17.0000 24.0000 1.0000 8.0000 15.0000 0 -27.4706 5.6471 3.1765 -4.2941 0 0 12.8373 18.1585 18.4154 0 0 0 -9.3786 -31.2802 0 0 0 0 90.1734 >> A-L*U ans = 1.0e-014 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3553 0 0 0 0 0 0 0 0.3553 0 0 We can see again in this example that L is lower triangular and that U is upper triangular and that L*U does equal A because the exponent is extremely small.--------------------------------------------------------------------------------------------------------------------------------------- 2. function [x,count] = ppmysolve(A,b) m = size(A,1); n = size(A,2); x = zeros(n,1); count=0; %Bad Gauss code A=[A b]; for i=1:m-1 [r,k]=max(abs(A(i:m,i))); if (k ~= 1) count=count+1; temp=A(i+k-1,:); A(i+k-1,:)=A(i,:); A(i,:)=temp; end for j=i+1:m A(j,:)=A(j,:)-(A(j,i)/A(i,i))*A(i,:); end end b = A(:,n+1); B = A(1:m,1:n); %x = backsub(B,b); for i=n:-1:1 x(i)=(b(i)-B(i,:)*x)/B(i,i); end--------------------------------------------------------------------------------------------------------------------------------------...
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Project 3 Solutions - Project 3 Group name: Unknowns Group...

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