In this paper, a block-based watermarking scheme based on the Singular Value Decomposition (SVD) is proposed. Our watermark, a pseudo-random Gaussian sequence, is embedded by modifying the angles formed by the right singular vectors of each block of the original image. The orthogonality property of the right singular vector matrix is preserved during the embedding process. Several experiments h...

For Ax = b, it has recently been reported that the convergence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type P = I + S (α) to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this paper, we discuss the adaptive Gauss-Seidel iterative method which uses P = I + S (α) + K̄ (β) as a preconditioner. We present some com...

We present a new combinatorial algorithm for Boolean matrix multiplication that runs in O(n(log log n)/ log n) time. This improves the previous combinatorial algorithm by Bansal and Williams [FOCS’09] that runs in O(n(log log n)/ log n) time. Whereas Bansal and Williams’ algorithm uses regularity lemmas for graphs, the new algorithm is simple and uses entirely elementary techniques: table looku...

We study the implementation of dense linear algebra computations, such as matrix multiplication and linear system solvers, on two-dimensional (2D) grids of heterogeneous processors. For these operations, 2D-grids are the key to scalability and eÆciency. The uniform block-cyclic data distribution scheme commonly used for homogeneous collections of processors limits the performance of these opera...

We present some observations on a restricted variant of unitary Cayley graphs modulo n, and implications for a decomposition of elements of symplectic operators over the integers modulo n. We define quadratic unitary Cayley graphs Gn, whose vertex set is the ring Zn, and where residues a, b modulo n are adjacent if and only if their difference is a quadratic residue. By bounding the diameter of...

The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N−particle systems on a line for the case of separable center-of-mass motion. New decomposition of the superhamiltonian into block-diagonal form with elementary matrix components is constructed. Matrices of coefficients of these minimal blocks are shown to coincide with matrices of irreduci...