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{"id":733,"date":"2023-05-03T18:12:46","date_gmt":"2023-05-03T22:12:46","guid":{"rendered":"https:\/\/rainyuxuan.com\/?p=733"},"modified":"2023-11-24T19:03:49","modified_gmt":"2023-11-25T00:03:49","slug":"cholesky-factorization-and-elimination-tree","status":"publish","type":"post","link":"https:\/\/rainyuxuan.com\/posts\/cholesky-factorization-and-elimination-tree\/","title":{"rendered":"Cholesky Factorization and Elimination Tree"},"content":{"rendered":"\n
In the last chapter, we introduced the concept of dependency. In this chapter, we will look into it and see how we can utilize this concept in factorization.<\/p>\n\n\n\n
Left-looking Cholesky factorization<\/h2>\n\n\n\n
Particularly, we will use the Left-Looking Cholesky Factorization<\/em><\/strong>. In the left-looking Cholesky factorization, we compute the factor column-by-column from left to right, using the already computed information (, , and in the figure below).<\/p>\n\n\n\n