Physical Sciences and Mathematics Commons^™

Wavelet Factorization Via A Homogenization Analogy For Solutions Of Linear Systems, Andrea Van Sickle

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A system of linear equations can be solved using a factorization method that produces a wavelet structure and is akin to a homogenization process used in determining the solution of differential equations. The method is dependant on the particular structure of Hadamard matrices and their implementation in a similarity transform. This paper details the development of such a method for systems of size 2n x 2n, including establishing the theoretical underpinnings necessary to define an orthogonal transform. Also, we present the development of an algorithm to implement the method for a simple 2 x 2 system, which will then be …