An Approximate Singular Value Decomposition of Large Matrices in Julia

In this project, I implement a parallel approximate singular value decomposition (SVD) in Julia. The approach taken here follows the algorithm described by Friedland et al., [1] and implement it using AbstractMatrices and DArrays in Julia to give the user additional flexibility. For additional speed, the algorithm makes direct calls to the DGEMV routine in the BLAS kernels. An error analysis using (1) random matrices drawn from a uniform distribution, (2) random matrices drawn from a normal distribution, and (3) a real image is performed to quantify the error induced by using the approximate algorithm. The error is found to be less than 6% and the algorithm exhibits good scaling for large matrices. This algorithm is ready to be used by other Julia users and can be found online at https://github.com/alexjturner/SVDapprox.