Discrete Calculus Applied Analysis on Graphs for Computational Science /

• Main Authors: Grady, Leo J. (Author), Polimeni, Jonathan R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: London : Springer London : Imprint: Springer, 2010.
• Subjects: Computer science.; Computer vision.; Computer science > Mathematics.; Computer Science.; Image Processing and Computer Vision.; Computational Mathematics and Numerical Analysis.; Theoretical, Mathematical and Computational Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-84996-290-2

The field of discrete calculus, also known as "discrete exterior calculus", focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space. In contrast to traditional goals of fin...

Table of Contents:

• Discrete Calculus: History and Future
• Part I: A Brief Review of Discrete Calculus
• Introduction to Discrete Calculus
• Circuit Theory and Other Discrete Physical Models
• Part II: Applications of Discrete Calculus
• Building a Weighted Complex from Data
• Filtering on Graphs
• Clustering and Segmentation
• Manifold Learning and Ranking
• Measuring Networks
• Representation and Storage of a Graph and Complex
• Optimization
• The Hodge Theorem: A Generalization of the Helmholtz Decomposition.