In the article Topology Testing of Phylogenies Using Least Squares methods, Aleksandra Czarna et al. use the least squares method to analyze data from a variety of biology topics including mammalian mitochondrial protein sequences, nucleotides, Hepatitis C, and DNA hybridization. The researchers found that the weighted least squares method provides a computationally efficient approximation to the generalized least squares method. This was particularly useful when analyzing sets of trees, and when assessing the phylogenetic signal in the data when other methods are not available.

            It is easy to see that this topic ties into the topics of the CS 322 course Scientific Computing. In the course, we learn about a lot of methods and one of these happens to be the least squares method. However, we do not get to see much of the methods we learn in practice. This article shows how the use of the least squares method can be very beneficial for the analysis of Biomedical data. The authors point out that they used the weighted least squares method because it was both computationally efficient and it gave a great approximation to the generalized least squares method. That is exactly what this course is about, methods to guarantee computations that a extremely close to optimal if not optimal, while still taking in consideration computational efficiency. There seems to be a trade-off in the amount of error a method has and its efficiency.

            This article may not be the most exciting read, but it shows that there is a use for the Least Squares method out there. In one of the author’s studies, they analyzed a set of mammalian mitochondrial protein data that included 3414 aligned amino acids from the cow, harbor seal, human, mouse, opossum, and rabit. They used generalized least squares in a program to construct a confidence set of trees to analyze this data. They used similar techniques for studying Hepatitis C, and DNA hybridization data. So in conclusion, there are uses for the least squares method out there and scientific computing is cool.