Incomplete LU Step

Problem

Compute the diagonal of U in the ILU(0) factorization of a tridiagonal matrix A.

Set u[0] = A[0][0], then for each i > 0 use multiplier l = A[i][i-1] / u[i-1] and u[i] = A[i][i] - l * A[i-1][i]. Return the list of u values.

Hint

ILU(0) keeps the sparsity pattern of A while producing approximate factors.

case 1

in: [[[4,1,0],[1,4,1],[0,1,4]]]

expected: [4,3.75,3.7333333333333334]

case 2

in: [[[2,0],[0,2]]]

expected: [2,2]

case 3

in: [[[1,1],[1,2]]]

expected: [1,1]

case 4

in: [[[4,2],[2,5]]]

expected: [4,4]

Starter codePython

def ilu0_tridiagonal(A):
    # Your code here
    pass

4 test cases · run your code against them in the editor