The book Kernel-Based Approximation Methods Using MATLAB, co-written by Greg Fasshauer, associate chair and professor of applied mathematics at IIT, and Mike McCourt (AMAT ’07), will be published this month by World Scientific. The book is based on a research project that the two began work on while McCourt was an undergraduate at Illinois Tech. They continued this work after McCourt graduated, while he worked at Argonne National Laboratory, earned his Ph.D. at Cornell University, and joined University of Colorado at Denver as a visiting assistant professor.
The book discusses recent advances in the theory and implementation of positive definite kernels. As the scientific community continues to realize the benefits of working with big data, the need for efficient tools to analyze high-dimensional problems becomes increasingly evident. Positive definite kernels, certain types of which are also known as radial basis functions, are useful tools for this purpose. In their book, Fasshauer and McCourt explore the historical development of both the mathematical and statistical foundations of these methods, and then discuss modern methods for accurate and stable computation with positive definite kernels. They also provide a software library for readers who are interested in adapting their presentation to their own applications.
McCourt has left academia and now works at SigOpt, a Silicon Valley start-up that specializes in the optimization of models for machine learning, computer simulations, and physical experiments.