Monotone systems of polynomial equations (MSPEs) are systems of fixedpoint equations X1 = f1(X1, . . . , Xn), . . . , Xn = fn(X1, . . . , Xn) where each fi is a polynomial with positive real coefficients. The question of computing the least non-negative solution of a given MSPE X = f (X) arises naturally in the analysis of stochastic models such as stochastic context-free grammars, probabilisti...

Future 4th Generation (4G) wireless multiuser communication systems will have to provide advanced multimedia services to an increasing number of users, making good use of the scarce spectrum resources. Thus, 4G system design should pursue both highertransmission bit rates and higher spectral efficiencies. To achieve this goal, multiple antenna systems are called to play a crucial role. In this ...

It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras—that is, the algebraic models of the Intuitionistic Propositional Calculus—always exist, even when these algebras are not complete as lattices. The reason is that these extremal fixed-points are definable by formulas of the IPC. Consequently, the μ-calculus based on intuit...

Empirical Colebrook equation implicit in unknown flow friction factor (λ) is an accepted standard for calculation of hydraulic resistance in hydraulically smooth and rough pipes. The Colebrook equation gives friction factor (λ) implicitly as a function of the Reynolds number (Re) and relative roughness (ε/D) of inner pipe surface; i.e. λ0=f(λ0, Re, ε/D). The paper presents a problem that requir...

An important problem that arises in different areas of science and engineering is that of computing limits of sequences of vectors fxmg, where xm 2C, and the dimension N is very large in many applications. Such vector sequences arise, for example, in the numerical solution of very large systems of linear or nonlinear equations by fixedpoint iterative methods, and limm!1xm are simply the require...

z990 floatingpoint unit G. Gerwig H. Wetter E. M. Schwarz J. Haess C. A. Krygowski B. M. Fleischer M. Kroener The floating-point unit (FPU) of the IBM z990 eServer is the first one in an IBM mainframe with a fused multiply-add dataflow. It also represents the first time that an SRT divide algorithm (named after Sweeney, Robertson, and Tocher, who independently proposed the algorithm) was used i...

In this paper, we present an automated technique swati: Synthesizing Wordlengths Automatically Using Testing and Induction, which uses a combination of Nelder-Mead optimization based testing, and induction from examples to automatically synthesize optimal fixedpoint implementation of numerical routines. The design of numerical software is commonly done using floating-point arithmetic in design-...

Abstract: The problem of robust dynamic pricing of an abstract commodity, whose inventory is specified at an initial time but never subsequently replenished, originally studied by Perakis and Sood (2006) in discrete time, is considered from the perspective of continuous time. We use a multiplicative demand function to model the uncertain demand, and develop a robust counterpart to replace the u...

We present what we call Constructive Default Logic (CDL) a default logic in which the fixedpoint definition of extensions is replaced by a constructive definition which yield so-called constructive extensions. Selection functions are used to represent explicitly the control of the reasoning process in this default logic. It is well-known that Reiter's original default logic lacks, in general, a...

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as forward-backward splitting (FBS) and Douglas-Rachford splitting (DRS), actually define a possibly semi-smooth and monotone fixed-point mapping; ii) The optimal solutions o...