Singular value decomposition transform with an FFT-based algorithm on the connection machine CM5

Abstract

We describe in this paper the parallel implementation of a modified, high radix fast Fourier transform (FFT) together with a Jacobi-based algorithm for matrix factorization to compute the singular value decomposition (SVD) of a 16384/spl times/16384 projection normal matrix arising from probability measure estimation in positron emission tomography (PET). We simplify the analysis significantly by working with block matrices and the Kronecker products because the symmetries built into the orthogonal decompositions allow the computation of the various factorizations of interest.