78 lines
1.0 KiB
Matlab
78 lines
1.0 KiB
Matlab
%% Problem 1
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clear all;
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clc;
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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 = Alg5([A b])
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%% Problem 2
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clear all;
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clc;
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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(A);
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b = P*b;
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% Ly = b and Ux = y
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y = Alg3(L, b); % Forward substitution
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x = Q*Alg4(U, y) % Backward substitution
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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 = Alg5([A b])
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Bp = Alg5([A bp])
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%% Problem 5
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clear all;
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clc;
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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(A)
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I = P*eye(3);
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% Ly = b and Ux = y
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y = Alg3(L, I); % Forward substitution
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x = Q*Alg4(U, y) % Backward substitution
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inv(A) - x
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%% Problem 6
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clc;
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A = [1 2 3 4;
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-1 1 2 1;
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0 2 1 3;
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0 0 1 1];
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[L, U, P] = Alg8(A)
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det(A) - prod(diag(U))
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%% Problem 10
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% A = [1 2 2 3 1;
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% 2 4 4 6 2;
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% 3 6 6 9 6;
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% 1 2 4 5 3]
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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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Alg6_RREF([A b])
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