[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.