82 lines
1.2 KiB
Matlab
82 lines
1.2 KiB
Matlab
clear all;
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A = [2, -1, 0, 0;
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-1, 2, -1, 0;
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0, -1, 2, -1;
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0, 0, -1, 2];
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b = [0;0;0;5];
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B = Alg1_outer_product_gaussian_elimination(A);
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U = triu(B);
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L = tril(B, -1);
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x = back_substitution(U, b);
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%% Problem 1
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clear all;
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A = [2, -1, 0, 0;
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-1, 2, -1, 0;
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0, -1, 2, -1;
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0, 0, -1, 2];
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b = [0;0;0;5];
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B = gauss_jordan_elimination([A b])
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[P, Q, L, U] = Alg2_gaussian_elimination_with_complete_pivoting(A);
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b = P*b;
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% Ly = b and Ux = y
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y = forward_substitution(L, b);
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x = Q*back_substitution(U, y);
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% L*U
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%% Problem 2
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A = [1, 1, 1;
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1, 1, 2;
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1, 2, 2];
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b = [1;2;1];
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[P, Q, L, U] = Alg2_gaussian_elimination_with_complete_pivoting(A);
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b = P*b;
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% Ly = b and Ux = y
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y = forward_substitution(L, b);
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x = Q*back_substitution(U, y)
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% L*U
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%% Problem 4
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A = [0.835, 0.667;
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0.333, 0.266];
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b = [0.168; 0.067];
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bp = [0.168; 0.066];
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kappa = cond(A)
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B = gauss_jordan_elimination([A b])
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Bp = gauss_jordan_elimination([A bp])
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%% Problem 5
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% AX = I3
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A = [2, 1, 2;
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1, 2, 3;
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4, 1, 2];
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[P, Q, L, U] = Alg2_gaussian_elimination_with_complete_pivoting(A);
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I = P*eye(3);
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% Ly = b and Ux = y
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y = forward_substitution(L, I);
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X = Q*back_substitution(U, y)
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inv(A)
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%% Problem 6
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