The efficiency of the one-sided parallel block-Jacobi algorithm for computation of the singular value decomposition (SVD) of a general matrix A ∈ Rm×n, m ≥ n, depends–besides some numerical tricks that speed-up the convergence–crucially on the parallel ordering of subproblems, which are to be solved in each parallel iteration step. We discuss in detail possible generalizations of the so-called ...

Abstract. Suppose A = (aijk) ∈ Rn×n×n is a three-way array or third-order tensor. Many of the powerful tools of linear algebra such as the singular value decomposition (SVD) do not, unfortunately, extend in a straightforward way to tensors of order three or higher. In the twodimensional case, the SVD is particularly illuminating, since it reduces a matrix to diagonal form. Although it is not po...

The singular value decomposition (SVD) of a 2-by-2 complex matrix does not occur as frequently as that of a 2-by-2 real upper triangular matrix. The commonly used QR method for SVD consists of two stages. In the first stage, a matrix is reduced to bidiagonal form using, say, Householder transformations on both sides. In the second stage, the bidiagonal matrix resulted from the first stage is di...

A novel algorithm is presented for adaptive eigennltering and for updating the singular value decomposition (SVD). It is an improvement upon an earlier developed Jacobi-type SVD updating algorithm, where now the exact orthogonality of the matrix of singular vectors/eigenvectors is guaranteed by storing a minimal factorization. This orthogonality property is known to be crucial for the numerical...

Mammography is the only effective and viable technique to detect breast cancer especially in the case of minimal tumors. About 30% to 50% of breast cancers demonstrate deposits of calcium called micro calcifications. Our method proposes an approach for detecting microcalcification in mammograms based on combined feature set with Support Vector Machine (SVM) classifier. The diagonal matrix ̳S‘ o...

Since the stage of diagonalization of Jacobi–type methods is difficult to monitor in a parallel environment, it is usually proposed to execute a predetermined number of sweeps (iterations) on a parallel processor array. A possibility for monitoring the stage of diagonalization is essential in order to avoid the execution of a significant number of unnecessary sweeps. Based on a Lemma used for a...

This thesis presents a systolic algorithm for the SVD of arbitrary complex matrices, based on the cyclic Jacobi method with \parallel ordering". As a basic step in the algorithm, a two-step, two-sided unitary transformation scheme is employed to diagonalize a complex 2 2 matrix. The transformations are tailored to the use of CORDIC (COordinate Rotation Digital Computer) algorithms for high spee...

Abstract: We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to devise an inversion procedure which has the advantages of localization and multiscale analysis of wavelet representations without losing the stability and computability of the SVD decompositi...

In earlier reports, a Jacobi-type algorithm for SVD updating has been developed 8] and implemented on a systolic array 9]. Here, this is extended to a generalized decomposition for a matrix pair, viz. the quotient singular value decomposition (QSVD). Updating problems are considered where new rows are appended to either one or both of the matrices involved. Systolic arrays as well as square roo...

We describe three new Jacobi orderings for parallel computation of SVD problems on tree architectures. The rst ordering uses the high bandwidth of a perfect binary fat-tree to minimise global interprocessor communication costs. The second is a new ring ordering which may be implemented e ciently on an ordinary binary tree. By combining these two orderings, an e cient new ordering, well suited f...