PERFORMANCE ANALYSIS OF QR AND CHOLESKY FACTORIZATIONS USING INDEXED DATA STRUCTURES AND LINKED LISTS (Interdisciplinary Studies Journal, 2026)
Numerous real-world problems in the fields of physics, chemistry, and engineering involve large-scale sparse linear systems composed of thousands of equations. In some cases, these systems admit a unique solution that can be obtained through direct methods. Among these, methods based on matrix factorization, such as QR and Cholesky factorizations, are particularly noteworthy. These methods aim to obtain a solution that is very close to the exact one in a limited number of steps. This study presents the implementation and analysis of the QR and Cholesky factorization methods using indexed data structures and linked lists. The computational results indicate that the linked-list structure exhibited lower performance with the QR factorization, whereas the opposite was observed for the Cholesky method. However, in both methods, the use of linked lists resulted in lower memory consumption, proving to be an efficient and effective alternative for data storage.
Keywords: QR Factorization; Cholesky Factorization; Linked Lists; Sparse Matrices