Date of Award
Master of Science (MS)
Mathematics and Statistics
Joseph V. Koebbe
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 the basic building block for developing algorithms to solve higher-ordered systems.
Sickle, Andrea Van, "Wavelet Factorization via a Homogenization Analogy for Solutions of Linear Systems" (2005). All Graduate Plan B and other Reports. 1283.
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