# Preprocessing algorithm for the generalized SVD on the graphics processing units

Flegar, Goran (2016) Preprocessing algorithm for the generalized SVD on the graphics processing units. Diploma thesis, Faculty of Science > Department of Mathematics.

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Language: English

In this thesis we study a preprocessing algorithm for the generalized SVD and its parallelization on the graphics processing unit. The preprocessing algorithm reduces a general matrix pair (A; B) to an upper triangular matrix pair ($\tilde{A}, \tilde{B}$) where B is nonsingular. After the preprocessing step a specialized algorithm, such as the implicit Kogbetliantz or the Hari–Zimmerman algorithm, which requires this structure of the matrix pair can be used to compute the generalized SVD. In the first chapter of the thesis we define the generalized SVD and describe the upper triangular decomposition resulting from the preprocessing step. Additionally, we describe the complete orthogonal decomposition which is used in the preprocessing step. The second chapter describes the challenges that arise when developing algorithms for the GPU and presents an efficient implementation of the preprocessing step. In the final chapter we test the algorithm on a variety of matrices of different sizes and compare the speed, rank detection, backward error and the effect on generalized singular values of our algorithm and LAPACK’s and MKL’s versions of xGGSVP.