Computing with Infinite and Infinitesimal Numbers in Matlab easily: The Grossone-Light Toolbox

The introduction of the novel numeral system introduced in [1] (based on the notion of grossone) opens new frontiers in numerical computing, allowing to easily perform computations involving infinite and infinitesimal numbers in a numerical way. This work is aimed at making this powerful numeral system easily usable and accessible to the large community of Matlab users. We have implemented (using pure Matlab code) the GrossoneLight Matlab Toolbox, a collection of classes, functions and examples that make grossone-based computing straightforward. The toolbox is called "light" because it introduces some limitations to the more general numeral system discussed in [1]. In particular, only numbers made of integer powers of grossone can be represented, together with bound on the minimum and maximum number of such powers. However, even in presence of such limitations, the implemented numeral system is powerful enough to solve basic numerical linear algebra problems. Following the Matlab object-oriented abstraction paradigm, available in latest Matlab releases, we have been able to implement two classes: the GrossNumber class and the GrossArray class. The first class allows to represent a number made of integer grossone powers, where the coecient used as multiplier for each power is a standard double-precision Matlab oating-point number. The GrossNumber class has been equipped with basic operations (addition, multiplication, etc) by operator overloading. This allows to operate on GrossNumber objects as any other Matlab scalar variable. The GrossArray class has been introduced to handle operations on arrays of GrossNumber objects more eciently. The speedup can be signicant, especially when the code is written in a vectorized fashion and a GPGPU (General Purpose Graphics Processing Units) is available on the machine running the toolbox.