Sparse matrix storage and LU factorization are numerical-methods techniques for solving large systems of linear equations of the form Ax = B efficiently, applicable wherever a coefficient matrix is large but has very few nonzero entries per row. The core principle exploits sparsity by storing only nonzero elements via compact linked-list representations, and by reordering rows and columns (static or dynamic ordering by row valence) to minimize "fill-in" during elimination, while LU factorization decomposes the matrix into lower- and upper-triangular factors so that repeated solves against a constant matrix avoid redundant computation. This is a topic in numerical linear algebra and computational methods, applied here within power systems engineering to iterative solution methods for large-scale networks.
Sparse matrix storage and LU factorization are numerical-methods techniques for solving large systems of linear equations of the form Ax = B efficiently, applicable wherever a coefficient matrix is l…