Using QMDD in Numerical Methods for Solving Linear Differential Equations via Walsh Functions

Abstract

This paper discusses the acceleration of computations involved in methods for solving a certain class of differential equations by Walsh series. These methods are based on computations with matrices of relatively large dimensions but having a block structure and including also the dyadic convolution matrices. We propose to represent the involved matrices by Quantum multiple-valued decision diagrams (QMDDs) and perform the computations over them. The structure of the matrices means the QMDDs are reasonably compact and therefore offer possibilities to speed up the overall computations as well as to work with matrices of large dimension which improves accuracy of the approximation of the required solutions by finite Walsh series.