The typical paradigm for obtaining a compressed version of a discrete signal represented by a vector x ∈ R is to choose an appropriate basis, compute the coefficients of x in this basis, and then retain only the k largest of these with k < N . If we are interested in a bit stream representation, we also need in addition to quantize these k coefficients. Assuming, without loss of generality, tha...

Given an i.i.d. sequence of n letters from a finite alphabet, we consider the length of the longest run of any letter. In the equiprobable case, results for this run turn out to be closely related to the well-known results for the longest run of a given letter. For coin-tossing, tail probabilities are compared for both kinds of runs via Poisson approximation.

In this paper, we introduce telescoping continued fractions to find lower bounds for the error term rn in Stirling’s approximation n!=2πnn+1/2e−nern. This improves given earlier by Cesàro (1922), Robbins (1955), Nanjundiah (1959), Maria (1965) and Popov (2017). The expression is terms of a fraction, together with an algorithm successive fraction. technique allows us experimentally obtain upper ...

We propose a fast first-order method to solve multi-term nonsmooth composite convex minimization problems by employing a recent proximal average approximation technique and a novel adaptive parameter tuning technique. Thanks to this powerful parameter tuning technique, the proximal gradient step can be performed with a much larger stepsize in the algorithm implementation compared with the prior...

In this paper we introduce the root of a fuzzy number, and we present aniterative method to nd it, numerically. We present an algorithm to generatea sequence that can be converged to n-th root of a fuzzy number.

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

Today’s most powerful supercomputers make use of many thousands or millions of parallel processors to achieve high speeds. However, some of the core solution algorithms in computational physics codes are not well suited to this environment. Linear scaling is generally lost as the number of processors becomes very large. New solution algorithms specifically designed for massively parallel execut...

Abstract—The Debye expansion integrals obtained by application of the Modified Watson Transformation and Debye series expansion to the Mie series for the high frequency plane wave transmitted into a double negative (DNG) cylinder are solved in the geometrically lit regions of the corresponding Debye series terms. The Debye series expansion is made up to the possible maximum term after which dou...