Title: A note on the boundary shape of matrix polytope products
Language: English
Authors: Bünger, Florian 
Keywords: Extreme points;Pointwise interval matrix products;Pointwise matrix polytope products
Issue Date: 2014
Publisher: [University of Louisiana at Lafayette]
Source: Reliable Computing 1 (20): 73-88 (2014)
Journal or Series Name: Reliable Computing 
Abstract (english): 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.
URI: http://hdl.handle.net/11420/7879
ISSN: 1573-1340
Institute: Zuverlässiges Rechnen E-19 
Type: (wissenschaftlicher) Artikel
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