Open AccessSignal processing of simplicial complexes
Author(s) -
С. Н. Чуканов
Publication year - 2022
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2182/1/012017
Subject(s) - curl (programming language) , simplicial manifold , mathematics , laplace transform , vector field , pure mathematics , decomposition , simplicial approximation theorem , simplicial complex , mathematical analysis , abstract simplicial complex , computer science , geometry , ecology , simplicial set , homotopy , homotopy category , biology , programming language
The paper considered the signal processing of simplicial complexes. Hodge decomposition formula for discrete fields is given, which is similar to the Hodge decomposition formula for smooth vector fields. The construction and the estimation of the gradient, divergence and curl operators and Laplace matrices for discrete vector fields are considered.