Algorithms for Matrix Approximations with Time Varying Systems

Abstract: There are different approaches to approximate matrices using structured matrices to reduce the computational cost of matrix-vector multiplications. A possible structure are sequentially semiseparable matrices, that describe the input-output behavior of time varying systems. If time varying systems are used to approximate weight matrices from neural networks, structural parameters have to be determined. In this thesis two algorithms to obtain the structural parameters are described. The first refines an initial segmentation by optimizing the input and output dimensions of the system. The second algorithm recursively splits the subsystems in a way that makes it possible to recover permuted sequentially semiseparable matrices. In experiments, the algorithms were able to recover the structure of simple test matrices. When used to approximate weight matrices from neural networks, the algorithms were able to reduce the computational cost of the matrix approximation compared to a naive approximation.

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