PERFORMANCE ANALYSIS OF QR AND CHOLESKY FACTORIZATIONS USING INDEXED DATA STRUCTURES AND LINKED LISTS

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Authors

DOI:

https://doi.org/10.56579/rei.v8i4.3124

Keywords:

QR Factorization, Cholesky Factorization, Linked Lists, Sparse Matrices

Abstract

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.

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Author Biographies

Débora Rezende Jalles, Fluminense Federal University

Master's degree in Computational Modeling in Science and Technology from Fluminense Federal University. Santo Antônio de Pádua, Rio de Janeiro, Brazil, 2025. Mathematics and Physical Sciences Teacher at the Municipal Department of Education of Itaperuna, Rio de Janeiro, Brazil.

Ricardo Silveira Sousa, Fluminense Federal University

Ph.D. in Computer Science and Computational Mathematics from the University of São Paulo (USP). Professor and permanent researcher in the Graduate Program in Computational Modeling in Science and Technology at Fluminense Federal University.

Thiago Jordem Pereira, Fluminense Federal University

Ph.D. in Computational Modeling from the Rio de Janeiro State University (UERJ). Has experience in the field of Mathematics, with an emphasis on Applied and Computational Mathematics, working mainly in the following areas: numerical and stochastic analysis, uncertainty quantification, fluid flow in porous media, and tumor growth modeling. Professor and permanent researcher in the Graduate Program in Computational Modeling in Science and Technology at Fluminense Federal University.

Wagner Rambaldi Telles, Fluminense Federal University

Ph.D. in Computational Modeling from the Rio de Janeiro State University (UERJ). Collaborating professor in the Professional Doctoral Program in Modeling and Technology for the Environment Applied to Water Resources (AmbHidro), offered by the Fluminense Federal Institute (IFFluminense). Has experience in the field of Mathematics, with an emphasis on Applied Mathematics and Scientific Computing, working primarily in the areas of numerical analysis, inverse problems, and optimization, with applications to water resources modeling. Professor and permanent researcher in the Graduate Program in Computational Modeling in Science and Technology at Fluminense Federal University.

References

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Published

2026-07-21

How to Cite

Jalles, D. R., Sousa, R. S., Pereira, T. J., & Telles, W. R. (2026). PERFORMANCE ANALYSIS OF QR AND CHOLESKY FACTORIZATIONS USING INDEXED DATA STRUCTURES AND LINKED LISTS. Interdisciplinary Studies Journal, 8(4), 01–21. https://doi.org/10.56579/rei.v8i4.3124

Issue

Vol. 8 No. 4 (2026): JOURNAL OF INTERDISCIPLINARY STUDIES

Section

ARTICLES

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