A Jacobi method for signal subspace computation

The Jacobi method for singular value decomposition is well-suited for parallel architectures. Its application to signal subspace computations is well known. Basically the subspace spanned by singular vectors of large singular values are separated from subspace spanned by those of small singular values. The Jacobi algorithm computes the singular values and the corresponding vectors in random order. This requires sorting the result after convergence of the algorithm to select the signal subspace. A modification of the Jacobi method based on a linear objective function merges the sorting into the SVD-algorithm at little extra cost. In fact, the complexity of the diagonal processor cells in a triangular array get slightly larger. In this paper we present these extensions, in particular the modified algorithm for computing the rotation angles and give an example of its usefulness for subspace separation.