We consider the problem of minimizing an indefinite quadratic function over the nonnegative orthant, or equivalently, the problem of deciding whether a symmetric matrix is copositive. We formulate the problem as a difference of convex functions (d.c.) problem. Using conjugate duality, we show that there is a one-to-one correspondence between their respective stationary points and minima. We the...

We study a wide class of solvable PT symmetric potentials in order to identify conditions under which these potentials have regular solutions with complex energy. Besides confirming previous findings for two potentials, most of our results are new. We demonstrate that the occurrence of conjugate energy pairs is a natural phenomenon for these potentials. We demonstrate that the present method ca...

The conjugate gradient method applied to the normal equations (cgne) is known as one of the most efficient methods for the solution of (non-symmetric) linear equations. By stopping the iteration according to a discrepancy principle, cgne can be turned into a regularization method. We show that cgne can be accelerated by preconditioning in Hilbert scales, derive (optimal) convergence rates with ...

Computing quark propagators in lattice QCD is equivalent to solving large, sparse linear systems with multiple right-hand sides. Block algorithms attempt to accelerate the convergence of iterative Krylov-subspace methods by solving the multiple systems simultaneously. This paper compares a block generalisation of the quasi-minimal residual method (QMR), Block Conjugate Gradient on the normal eq...

This paper is devoted to the study of some preconditioners for the conjugate gradient algorithm used to solve large sparse linear and symmetric positive definite systems. The construction of a preconditioner based on the Gram–Schmidt orthogonalization process and the least squares method is presented. Some results on the condition number of the preconditioned system are provided. Finally, numer...

Cross phenomena, representing responses of a system to external stimuli, are ubiquitous from quantum macro scale. The Onsager theorem is often used describe them, stating that the coefficient matrix cross phenomena connecting driving forces and fluxes internal processes symmetric. Here we show this intrinsically diagonal when chosen gradients potentials drive their respective conjugate molar qu...

1 A computationally efficient preconditioned conjugate gradient algorithm with a symmetric suc2 cessive over-relaxation (SSOR) preconditioner for the iterative solution of set mixed model 3 equations is described. Potential computational saving of this approach are examined for an 4 example of single-step genomic evaluation of Australian sheep. Results show that the SSOR 5 preconditioner can su...

This paper illustrates how GPU computing can be used to accelerate computational fluid dynamics (CFD) simulations. For sparse linear systems arising from finite volume discretization, we evaluate and optimize the performance of Conjugate Gradient (CG) routines designed for manycore accelerators and compare against an industrial CPU-based implementation. We also investigate how the recent advanc...

It is very important for generating an orthonormal multiwavelet system to construct a conjugate quadrature filter (CQF). In this paper, a general method of constructing a length-J + 1 CQF with multiplicity r and scale a from a length-J CQF is obtained. As a special case, we study generally the construction of a length-J + 1 CQF with multiplicity 2 and scale 2 which can generate a compactly supp...

In this work we revisit TV filter and propose an improved version that is tailored to diagnostic CT purposes. We revise TV cost function, which results in symmetric gradient function that leads to more natural noise texture. We apply a multi-scale approach to resolve noise grain issue in CT images. We examine noise texture, granularity, and loss of low contrast in the test images. We also discu...