Het ontbinden van een matrix m.b.v. een getraind neuraal netwerk
S.R. Veldkamp (TU Delft - Electrical Engineering, Mathematics and Computer Science)
M Moller – Mentor (TU Delft - Numerical Analysis)
Yves Van Gennip – Graduation committee member (TU Delft - Mathematical Physics)
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Abstract
Before making matrix calculations, it can be useful to decompose these matrices in some way, such as according to an LU-decomposition. This can save a lot of computing power and thus time. Several computer programs exist that can decompose matrices in multiple ways. However, this report answers the question of whether it is also possible to make these decompositions in another way: namely with the help of a trained neural network. In this report is described how a trained neural network can help in finding LU decompositions of 2x2 matrices.
By making good use of the structure of a neural network, and by choosing a fitting optimizer, learning rate and loss function, a neural network can indeed quickly learn to make a LU-decomposition of a matrix. With this, it is readily shown that classical algorithms such as LU decompositions can be reproduced with trained neural networks.