A Fixed-point Model and Solution Algorithms for Simulating Urban Freight Distribution in a Multimodal Context

2011 ◽  
Vol 11 (4) ◽  
pp. 647-654 ◽  
Author(s):  
Luca D`Acierno ◽  
Mariano Gallo ◽  
Bruno Montella
Keyword(s):  
Fixed Point ◽  
Point Model ◽  
Urban Freight ◽  
Solution Algorithms

scholarly journals Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations

2020 ◽  
Vol 378 (2166) ◽  
pp. 20190052 ◽  
Author(s):  
Michael Hopkins ◽  
Mantas Mikaitis ◽  
Dave R. Lester ◽  
Steve Furber
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
High Performance ◽  
Floating Point ◽  
Double Precision ◽  
Least Significant Bit ◽  
Fixed Point Arithmetic ◽  
Solution Algorithms ◽  
Point Arithmetic

Although double-precision floating-point arithmetic currently dominates high-performance computing, there is increasing interest in smaller and simpler arithmetic types. The main reasons are potential improvements in energy efficiency and memory footprint and bandwidth. However, simply switching to lower-precision types typically results in increased numerical errors. We investigate approaches to improving the accuracy of reduced-precision fixed-point arithmetic types, using examples in an important domain for numerical computation in neuroscience: the solution of ordinary differential equations (ODEs). The Izhikevich neuron model is used to demonstrate that rounding has an important role in producing accurate spike timings from explicit ODE solution algorithms. In particular, fixed-point arithmetic with stochastic rounding consistently results in smaller errors compared to single-precision floating-point and fixed-point arithmetic with round-to-nearest across a range of neuron behaviours and ODE solvers. A computationally much cheaper alternative is also investigated, inspired by the concept of dither that is a widely understood mechanism for providing resolution below the least significant bit in digital signal processing. These results will have implications for the solution of ODEs in other subject areas, and should also be directly relevant to the huge range of practical problems that are represented by partial differential equations. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

scholarly journals A fixed point model for rate control and routing in cloud data center networks

2013 ◽  
Vol 7 (9) ◽  
pp. 1420-1436
Author(s):  
Bo Li ◽  
Xuefeng Ma ◽  
Jianming Li ◽  
Zhou Zong
Keyword(s):  
Fixed Point ◽  
Rate Control ◽  
Data Center ◽  
Data Center Networks ◽  
Point Model ◽  
Cloud Data Center ◽  
Cloud Data
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