| Summary: | <div><p class="IEEEAbtract"><em>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 </em><em>it is necessary to do an analysis of which method is </em><em>the </em><em>best so that the user can choose the most efficient method. The method</em><em>s that will be </em><em>analyzed </em><em>are </em><em>LU, Crout, Cholesky decomposition</em><em>, and </em><em>QR factorization. From the calculation of arithmetic operations obtained Cholesky decomposition method is the most efficient method because it has the fewest arithmetic operations.</em><em> Further, to verify the proposed method we demonstrated s</em><em>imulation with a case study of the relationship between carbon and nitrogen </em><em>with</em><em> the </em><em>macrobenthos</em><em> diversity</em><em> based on data from </em><em>the area of polyculture system and PT. Kayu Lapis Indonesia coastal, Mororejo village subdistrict Kaliwungu district Kendal</em><em>. From the s</em><em>imulation result</em><em>sis</em><em> obtained </em><em>that </em><em>computing</em><em> time</em><em> 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.</em><em></em></p></div> <p>Keywords<em>—</em><em> LU</em><em> </em><em>Decomposition, Crout decomposition, QR factorization, Ch</em><em>o</em><em>l</em><em>e</em><em>sky decomposition, Carbon, Nitrogen, Ma</em><em>c</em><em>robent</em><em>h</em><em>os</em><em></em></p>
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