In this talk I will present work in my group towards improving the efficiency of two popular algorithms for treating the electronic structure of materials (a) the density functional theory (DFT) and (b) a flavor of quantum Monte Carlo theory known as auxiliary field quantum Monte Carlo (AFQMC). I will begin by giving a general outline of the two algorithms including their strengths and limitations. I will follow this with a description of the techniques that are used to improve the efficiency of these methods. For DFT we make use of Interpolative decomposition in addition to robust fitting. For AFQMC we make use of the generalized Wick's theorem and techniques from local correlation. I will finish by giving some applications of these algorithms.