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A note on the boundary shape of matrix polytope products
Publikationstyp
Journal Article
Date Issued
2014
Sprache
English
Author(s)
Institut
TORE-URI
Journal
Volume
20
Issue
1
Start Page
73
End Page
88
Citation
Reliable Computing 1 (20): 73-88 (2014)
Scopus ID
Publisher
[University of Louisiana at Lafayette]
Motivated by interval matrix multiplication we consider (matrix) polytopes A ⊆ ℝm,n, B ⊆ ℝn,k, m, n, k ∈ ℕ, and investigate the boundary shape of their pointwise product AB:= AB | A ∈ A,B ∈ B: We prove that AB cannot have outward curved boundary sections while inward curved sections may exist. This is achieved by a simple local extreme point analysis. Results are proved in a more general abstract setting for images of compact sets of (not necessarily finite dimensional) locally convex vector spaces under continuous multilinear mappings. They can be seen as extensions of the Zadeh-Desoer Mapping Theorem which is a fundamental tool in control theory.
Subjects
Extreme points
Pointwise interval matrix products
Pointwise matrix polytope products
DDC Class
004: Informatik
510: Mathematik