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Crout's algorithm works just fine

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This commit is contained in:
Sergiusz Warga 2021-03-13 19:02:40 +01:00
parent f2fc11bfc0
commit d6b6b159af
2 changed files with 29 additions and 8 deletions
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10
Direct Methods for Solving Linear Systems/Alg1_outer_product_gaussian_elimination.m
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@ -1,9 +1,9 @@
function A = Alg1_outer_product_gaussian_elimination(A)
% ADDME Algorithm 1: Outer Product Gaussian Elimination (Golub, Loan, 3.2.1)
% Matrix A has to be a square singular matrix.
[n, m] = size(A);
if n ~= m
[m, n] = size(A);
if m ~= n
error('Matrix is not squared!')
end
@ -11,8 +11,8 @@ end
% error('Matrix is not nonsingular!')
% end
for k = 1 : n-1
rows = k + 1 : n;
for k = 1 : m-1
rows = k + 1 : m;
A(rows, k) = A(rows, k)/A(k, k);
A(rows, rows) = A(rows, rows) - A(rows, k) * A(k, rows);
end

27
Direct Methods for Solving Linear Systems/Alg7.m
View File

@ -5,9 +5,30 @@ function [L, U] = Alg7(A)
[m, n] = size(A);
A = Alg1_outer_product_gaussian_elimination(A);
% This solution is mathematically correct, however computationaly
% inefficient.
%
% A = Alg1_outer_product_gaussian_elimination(A);
%
% U = triu(A);
% L = tril(A, -1) + eye(m);
U = triu(A);
L = tril(A, -1) + eye(m);
% Instead, we should use the Crout's algorithm
% It returns an Unit Upper Triangular matrix and a Lower Traingular matrix
% (in oppose to the Gaussian Elimination).
A
L = zeros(m, n)
U = eye(m, n)
for k = 1:n
for i = k:n
L(i, k) = A(i, k) - dot(L(i,1:k-1), U(1:k-1, k));
end
for j = k : n
U(k, j) = (A(k, j) - dot(L(k, 1:k-1), U(1:k-1, j))) / L(k, k);
end
end
end