Polynomial-Based Approach for Efficient Function Computation of Symmetric Matrices Using Restarted Heavy Ball Method

Abstract

This paper presents a polynomial-based approach for efficiently computing functions of symmetric matrices by leveraging the Restarted Heavy Ball (RHB) method. The RHB method is employed to overcome the slow convergence issue commonly encountered when computing functions of symmetric matrices. The key idea of our approach is to approximate the desired function using a polynomial. By representing the function as a polynomial, we can leverage the efficient computation of polynomials to accelerate the overall function computation process. We introduce a systematic methodology for constructing an optimal polynomial approximation that minimizes the approximation error. To further enhance the convergence speed, we incorporate the Restarted Heavy Ball method into our polynomialbased approach. The Restarted Heavy Ball iteration is applied after a certain number of iterations to reset the computation process and mitigate the slow convergence behavior. The experimental results and analysis validate the effectiveness and practicality of our approach, highlighting its potential for various applications involving function computations of symmetric matrices. Overall, our polynomial-based approach, integrated with the Restarted Heavy Ball method, offers an efficient and accurate solution for computing functions of symmetric matrices. The experimental results and analysis validate the effectiveness and practicality of our approach, highlighting its potential for various applications involving function computations of symmetric matrices.