From positional representation of numbers to positional representation of vectors

2023/03/17 by Izabella Ingrid Farkas, Edita Pelantová, Farkas, Izabella Ingrid +3
Computer Science · #Numerical Methods and Algorithms #Matrix Theory and Algorithms #Digital Filter Design and Implementation

paper · pdf · doi:10.48550/arxiv.2303.10027

Abstract

To represent real m-dimensional vectors, a positional vector system given by a non-singular matrix M ∈ ℤ^{m × m} and a digit set D ⊂ ℤ^m is used. If m = 1, the system coincides with the well known numeration system used to represent real numbers. We study some properties of the vector systems which are transformable from the case m = 1 to higher dimensions. We focus on algorithm for parallel addition and on systems allowing an eventually periodic representation of vectors with rational coordinates.

Related

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