[FEATURE REQUEST] Add LU decomposition algorithm for matrix (java) (hactoberfest'25)

[sourav-625]

What would you like to Propose?

I would like to propose the addition of LU decomposition algorithm under src/main/java/com/thealgorithms/matrix

This algorithm is widely used in:

• Solving systems of linear equations (Ax = b)
• Finding matrix inverses
• Computing determinants efficiently

Issue details

The above mentioned algorithm decomposes a square matrix A into product of 2 matrices:

A = L * U

where:

• L is a lower triangular matrix with 1s on its diagonal
• U is an upper triangular matrix

Example:
Matrix:
A = {
{2, -1, -2},
{-4, 6, 3},
{-4, -2, 8}
}

Expected Output:
L = {
{1.000, 0.000, 0.000},
{-2.000, 1.000, 0.000},
{-2.000, -1.000, 1.000}
}

U = {
{2.000, -1.000, -2.000},
{0.000, 4.000, -1.000},
{0.000, 0.000, 3.000}
}

Time Complexity: O(n^3)

Reference: https://en.wikipedia.org/wiki/LU_decomposition

Additional Information

No response

[sourav-625]

I would like to be assigned this issue, as I have already solved it. My Java program implementing this algorithm is neat and efficient.

[thanay2007]

I would like to work on this.