feat(maths): add LU decomposition algorithm using Doolittle method

[MD-Mushfiqur123]

Describe your change:

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
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• Documentation change?

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LU Decomposition (Doolittle Algorithm)

Decomposes a square matrix A into a lower triangular matrix L and an upper triangular matrix U such that A = L * U.

What This Adds

LUDecomposition.java - Main algorithm implementation:

• \decompose()\ - Performs LU factorization using the Doolittle algorithm with combined L/U storage
• \getLowerMatrix()\ - Extracts L (unit lower triangular) from combined matrix
• \getUpperMatrix()\ - Extracts U (upper triangular) from combined matrix
• \solve()\ - Solves Ax = b via forward and back substitution

LUDecompositionTest.java - Unit tests:

• Tests for 3x3 and 2x2 matrix decomposition
• Identity matrix decomposition
• Non-square matrix rejection
• Singular matrix detection
• Linear system solving (2x2 and 3x3)

Algorithm

The Doolittle algorithm computes L and U iteratively:

• U[k][j] = A[k][j] - sum(L[k][s] * U[s][j]) for s < k
• L[i][k] = (A[i][k] - sum(L[i][s] * U[s][k])) / U[k][k] for s < k

Time: O(n^3) decomposition, O(n^2) solve | Space: O(n^2)

Reference

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