We have learned different methods for matrix factorization, though the various methods we have seen seem to have rather strict requirements. Most notably, Cholesky Factorization requires a matrix to be both symmetric and positive definite. Many matrices we have seen were not symmetric, and most of us can barely recall what an eigenvalue is, let […]

A Linear optimization problem consists of a linear objective function to be maximized or minimized and linear constraints in the form of inequalities or equalities. Many problems can be reduced to linear optimization problems, such as minimum cost network flow. A common algorithm for solving linear optimization problems is the simplex method. Due to the […]

We’ve looked at Newton’s Method solely for finding roots, but there are other applications. One other significant use is locating local extreme points. This is the basis for many Optimization Algorithms. For those unfamiliar, Optimization problems consist of decision variables who take numeric values, and an objective function, which is to be maximized or minimized. […]