Hadamard transform

About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.

The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates

Abstract: The Hadamard and SJT product of matrices are two types of special matrix product. The latter was first defined by Chen. In this study, they are applied to the differential quadrature (DQ) solution of geometrically nonlinear bending of isotropic and orthotropic rectangular plates. By using the Hadamard product, the nonlinear formulations are greatly simplified, while the SJT product approach minimizes the effort to evaluate the Jacobian derivative matrix in the Newton-Raphson method for solving the resultant nonlinear formulations. In addition, the coupled nonlinear formulations for the present problems can easily be decoupled by means of the Hadamard and SJT product. Therefore, the size of the simultaneous nonlinear algebraic equations is reduced by two-thirds and the computing effort and storage requirements are alleviated greatly. Two recent approaches applying the multiple boundary conditions are employed in the present DQ nonlinear computations. The solution accuracies are improved obviously in comparison to the previously given by Bert et al. The numerical results and detailed solution procedures are provided to demonstrate the superb efficiency, accuracy and simplicity of the new approaches in applying DQ method for nonlinear computations.

On new Hermite Hadamard Fejer type integral inequalities

Abstract: In this paper, we establish several weighted inequalities for some dif- ferantiable mappings that are connected with the celebrated Hermite-Hadamard Fejer type integral inequality. The results presented here would provide extensions of those given in earlier works. Mathematics Subject Classification (2010): 26D15.

Discovery of an Hadamard matrix of order 92

Abstract: An Hadamard matrix H is an n by n matrix all of whose entries are + 1 or — 1 which satisfies HH = n J, H being the transpose of H. The order n is necessarily 1, 2 or 42, with t a positive integer. R. E. A. C. Paley [3] gave construction methods for various infinite classes of Hadamard matrices, chiefly using properties of quadratic residues in finite fields. These constructions cover all values of 4 ^ 2 0 0 , except 4/ = 92, 116, 156, 172, 184, 188. Further constructions have been given by J. Williamson [5; 6] , A. Brauer [ l ] , M. Hall [2] and R. Stanton and D. Sprott [4]. Williamson's first paper gave an Hadamard matrix of order 172, incorporating a special automorphism of order 3. The same method may be applied to 92, 116, 156, and 188, but Williamson did not do so, principally because of the amount of computation involved. Williamson's method has been applied to 4^ = 92 using the IBM 7090 at the Jet Propulsion Laboratory. The matrix H has the form

Proximal point methods for quasiconvex and convex functions with Bregman distances on Hadamard manifolds

Abstract: This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on noncompact Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obtain the same convergence properties for the classical proximal method, applied to a class of quasiconvex problems. Finally, we give some examples of Bregman distances in non-Euclidean spaces.