Differential Methods for Multidimensional Visual Data Analysis

Benger, Werner; Heinzl, René; Hildenbrand, Dietmar; Weinkauf, Tino; Theisel, Holger; Tschumperlé, David

doi:10.1007/978-3-642-27795-5_35-5

Search citation statements

Order By: Relevance

Paper Sections

Select...

Full Homogeneous Multivectors1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 62 publications

(82 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also assume that all the elements of the homogeneous multivectors are non-zero. In most applications dealing with geometry such as [17,16,1], the multivectors contain only non-zero elements. We call a multivector with only a single grade and having non-zero coefficients only, a full homogeneous multivector.…”

Section: Full Homogeneous Multivectorsmentioning

confidence: 99%

Computational Aspects of Geometric Algebra Products of Two Homogeneous Multivectors

Breuils,

Nozick,

Sugimoto

2020

Preprint

View full text Add to dashboard Cite

Studies on time and memory costs of products in geometric algebra have been limited to cases where multivectors with multiple grades have only non-zero elements. This allows to design efficient algorithms for a generic purpose; however, it does not reflect the practical usage of geometric algebra. Indeed, in applications related to geometry, multivectors are likely to be full homogeneous, having their non-zero elements over a single grade. In this paper, we provide a complete computational study on geometric algebra products of two full homogeneous multivectors, that is, the outer, inner, and geometric products of two full homogeneous multivectors. We show tight bounds on the number of the arithmetic operations required for these products. We also show that algorithms exist that achieve this number of arithmetic operations.

show abstract

Section: Full Homogeneous Multivectorsmentioning

confidence: 99%