In this paper, we generalize John von Neumann’s Middle-Square Method (MSM) to canonical number systems (CNS). Additionally, present some observations and statistical tests of the sequences generated by described generators.

Recently, the existed proximal gradient algorithms had been used to solve non-smooth convex optimization problems. As a special nonsmooth convex problem, the singly linearly constrained quadratic programs with box constraints appear in a wide range of applications. Hence, we propose an accelerated proximal gradient algorithm for singly linearly constrained quadratic programs with box constraint...

Recently, Gregório and Oliveira developed a proximal point scalarization method (applied to multiobjective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et al. as regularization. In this work we propose a variation of this method, taking into account the regularization with logarithm and quasi-distance, wher...

A family of variable metric methods for convex constrained optimization was introduced recently by Birgin, Mart́ınez and Raydan. One of the members of this family is the Inexact Spectral Projected Gradient (ISPG) method for minimization with convex constraints. At each iteration of these methods a strictly convex quadratic function with convex constraints must be (inexactly) minimized. In the ca...

None of the usual floating point numerical techniques available for solving the quadratic matrix equation AX +BX +C = 0 with square matrices A,B, C and X, can provide an exact solution; they can just obtain approximations to an exact solution. We use interval arithmetic to compute an interval matrix which contains an exact solution to this quadratic matrix equation, where we aim at obtaining na...

None of the usual floating point numerical techniques available for solving the quadratic matrix equation AX +BX +C = 0 with square matrices A,B, C and X, can provide an exact solution; they can just obtain approximations to an exact solution. We use interval arithmetic to compute an interval matrix which contains an exact solution to this quadratic matrix equation, where we aim at obtaining na...

While the diagonalization of a quadratic bosonic form can always be done using a Bogoliubov transformation, the practical implementation for systems with a large number of different bosons is a tedious analytical task. Here we use the coupled cluster method (CCM) to exactly diagonalise such complicated quadratic forms. This yields to a straightforward algorithm which can easily be implemented u...

A unified quadratic semi-infinite programming approach is introduced to solve digital filter design problems with time or frequency-domain specification. An algorithm based on this approach is developed and the corresponding convergence result is presented. This computational method is then applied to the optimum filter design problems subject to time and frequency domain specifications, namely...