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
In the process of determining the regression parameter is used least squares method that produces systems of linear equations. Here will be studied how to determine the solutions of the system of linear equations. The system of linear equations can be solved by several methods, such as, the LU decomposition method (Chinchole and Bhadane, 2014), Crout decomposition (Supriyono and Daniel, 2005), QR factorization (Bojanczyk, et al., 1986; Rorres, 2004), and Cholesky Decomposition (Robert and Elizabeth , 1990).
Therefore, the assessment needs to be conducted to determine the most efficient method. One of the applications of mathematics in the field of ecology, in this case represents the relationship between organic matter, carbon and nitrogen to macrobenthos diversity. Animal abundance macrobenthos have a very strong relationship with the content of organic matter in sediments and sedimentary textures (Kinanti et al., 2014) This means organic materials such as carbon and nitrogen affect the macrobenthos abundance.