A Prolegomenon to Differential Equations and Variational Methods on Graphs
A Prolegomenon to Differential Equations and Variational Methods on Graphs
February 2025
Paperback
9781009346634
NZD$34.95
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Hardback
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.
Product details
February 2025Paperback
9781009346634
100 pages
229 × 152 mm
Not yet published - available from February 2025
Table of Contents
- 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.
