Linear Algebra, Mathematics, Math, Principal Component, Python.
U[j,k:n] -= L[j,k] * U[k,k:n] return L, U A = np.array([[2,1,1,0],[4,3,3,1],[8,7,9,5],[6,7,9,8]]).astype(np.float) L, U = LU(A) np.allclose(A, L @ U) True The LU factorization is useful! Solving Ax = b becomes LUx = b: find A = LU solve Ly = b solve Ux = y Work Work for Gaussian Elimination: 2.1/3