Analysis of Crout, Lu, Cholesky Decomposition, and QR Factorization: A Case Study On The Relationship Between Abiotic (Carbon and Nitrogen) and Biotic (Macrobenthos Diversity) Factors

Abstract

Many real world problems can be represented by a system of linear equations, such as in the field of ecology, i.e, the relationship of carbon and nitrogen with  macrobenthos  diversity. There are many methods to solve linear equations system, then it is necessary to do an analysis of which method is the best so that the user can choose the most efficient method. The methods that will be analyzed are LU, Crout, Cholesky decomposition, and QR factorization. From the calculation of arithmetic operations obtained Cholesky decomposition method is the most efficient method because it has the fewest arithmetic operations. Further, to verify the proposed method we demonstrated simulation with a case study of the relationship between carbon and nitrogen with the macrobenthos diversity based on data from the area of polyculture system and PT. Kayu Lapis Indonesia coastal, Mororejo village subdistrict Kaliwungu district Kendal. From the simulation resultsis obtained that computing time the smallest is the Cholesky decomposition is equal to 1.4664 seconds, which means that the Cholesky decomposition is the most efficient method than the method of LU, Crout decomposition and QR factorization.

Keywords— LU Decomposition, Crout decomposition, QR factorization, Cholesky decomposition, Carbon, Nitrogen, Macrobenthos