An algorithm for multipication of Kaluza numbers

TL;DR

This paper introduces a new, more efficient algorithm for multiplying Kaluza numbers, reducing the computational complexity by leveraging the structural properties of the matrix involved.

Contribution

The paper presents a novel algorithm that halves the number of multiplications needed for Kaluza number multiplication by exploiting matrix structure.

Findings

Reduces multiplications from 1024 to 512

Reduces additions from 992 to 576

Uses matrix structure to optimize computation

Abstract

This paper presents the derivation of a new algorithm for multiplying of two Kaluza numbers. Performing this operation directly requires 1024 real multiplications and 992 real additions. The proposed algorithm can compute the same result with only 512 real multiplications and 576 real additions. The derivation of our algorithm is based on utilizing the fact that multiplication of two Kaluza numbers can be expressed as a matrixvector product. The matrix multiplicand that participates in the product calculating has unique structural properties. Namely exploitation of these specific properties leads to significant reducing of the complexity of Kaluza numbers multiplication.