Study deals with implementations of fixed-point division modules based on different algorithms on basis of Xilinx FPGAs. We show that our implementation of the nonrestoring algorithm is significantly faster and smaller than the 32-bit IP Core “Pipelined Divider” from Xilinx. For example, the speed of the 32-bit designed module is almost 245 MHz vs. 193 MHz from Xilinx divider. Moreover, high-sp...

The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixedpoint iteration, we explore the use of Anderson acceleration (also knownas Anderson mixing) to improve the convergence. We compare the performance of the preconditioned Uzawa algorithm with and without acceleratio...

We present a novel algorithm for collision detection between two discretely oriented polytopes (k-DOPs). It is an application of the well known Separating Axes Test to k-DOPs and is implemented in fixed-point arithmetic. Hence, it lends itself very well to hardware implementation. In this report we focus on the derivation of the algorithm and an error-bound on the rounding-error produced by the...

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...

Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

This paper deals with optimization techniques that can make very large vocabulary voice dictation applications deployable on recent mobile devices. We focus namely on optimization of signal parameterization (frame rate, FFT calculation, fixedpoint representation) and on efficient pruning techniques employed on the state and Gaussian mixture level. We demonstrate the applicability of the propose...