Grant: Discovery Grants Program - Individual

This is a proposal for research on matrix equations and matrix functions. The matrix equations are useful in nano research, in the study of problems in automatic control, as well as in stochastic models for queueing problems arising in telecommunications, computer performance and inventory control. For each case, a particular matrix satisfying the matrix equation is of practical interst. My goal is to design efficient and reliable algorithms for finding the desired solution, to provide a careful mathematical analysis of these equations and the algorithms designed, and to turn these algorithms into computer codes that can be readily used by researchers in various areas. I will also use matrix equations to study quadratic eigenvalue problems that arise in many applications. For the study of matrix functions, my main objective is to prove a conjecture related to some numerical methods for the matrix p-th root, which is used, for example, in some financial applications. The successful completion of the proposed research will be a significant contribution to the theory and applications of matrix equations and matrix functions.