
A Prolegomenon to Differential Equations and Variational Methods on Graphs
Cambridge University Press
Published on 27. February 2025
Book
Hardback
100 pages
978-1-009-49465-6 (ISBN)
Description
The use of differential equations on graphs as a framework for the mathematical analysis of images emerged about fifteen years ago and since then it has burgeoned, and with applications also to machine learning. The authors have written a bird's eye view of theoretical developments that will enable newcomers to quickly get a flavour of key results and ideas. Additionally, they provide an substantial bibliography which will point readers to where fuller details and other directions can be explored. This title is also available as open access on Cambridge Core.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Illustrations
Worked examples or Exercises
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 10 mm
Weight
308 gr
ISBN-13
978-1-009-49465-6 (9781009494656)
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Schweitzer Classification
Other editions
Additional editions

Yves van Gennip | Jeremy Budd
A Prolegomenon to Differential Equations and Variational Methods on Graphs
Book
02/2025
Cambridge University Press
€26.90
Shipment within 15-20 days
Persons
Author
Delft University of Technology
California Institute of Technology
Content
1. Introduction; 2. History and literature overview; 3. Calculus on undirected edge-weighted graphs; 4. Directed graphs; 5. The graph Ginzburg-Landau functional; 6. Spectrum of the graph Laplacians; 7. Gradient flow: Allen-Cahn; 8. Merriman-Bence-Osher scheme; 9. Graph curvature and mean curvature flow; 10. Freezing of Allen-Cahn, MBO, and mean curvature flow; 11. Multiclass extensions; 12. Laplacian learning and Poisson learning; 13. Conclusions; Bibliography.