Homer Walker's research and teaching interests are generally in computational and applied mathematics. In recent years, his research has been mainly concerned with developing and analyzing numerical algorithms for solving systems of linear and nonlinear equations, especially the very large systems that arise in modeling complex physical phenomena such as fluid flow. Previous research interests include numerical methods for unconstrained optimization, differential equations, and statistical estimation. When possible, he likes to work with experts in other areas of science and engineering to explore the practical effectiveness of the algorithms that he studies. Much of his work has been done in collaboration with researchers at U.S. national laboratories who have extensive experience with both challenging applications and advanced hardware and software for high-performance computing.

Walker enjoys bringing insights gained through his research to his teaching. This is especially important in computational mathematics courses because of the very dynamic nature of the area. These courses typically attract students from many departments in addition to Mathematical Sciences, reflecting not only the importance of the subject to modern science and engineering, but also the ease of pursuing interdisciplinary study at WPI.