A new method is described for computing the singular value decomposition (SVD). It begins by computing the polar decomposition and then computes the spectral decomposition of the Hermitian polar factor. The method is particularly attractive for shared memory parallel computers with a relatively small number of processors, because the polar decomposition can be computed efficiently on such machines using an iterative method developed recently by the authors. This iterative polar decomposition method requires only matrix multiplication and matrix inversion kernels for its implementation and is designed for full rank matrices; thus the proposed SVD method is intended for matrices that are not too close to being rank-deficient. On the Kendall Square KSR1 virtual shared memory computer the new method is up to six times faster than a parallelized version of the LAPACK SVD routine, depending on the condition number of the matrix
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