Prolegomenon to Differential Equations and Variational Methods on - Graph

A bird's eye view of theoretical developments and concrete applications that will enable newcomers to get a flavour of key results. Provides an exhaustive, at the time of writing, 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.

List 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.

Product details

• Authors: Jeremy Budd, Jeremy (California Institute of Technology) Budd, Budd Jeremy, Yves van Gennip, Yves van Gennip, Yves (Delft University of Technology) Van Gennip
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 01.02.2025
• EAN: 9781009346634
• ISBN: 978-1-0-0934663-4
• No. of pages: 75
• Series: Elements in Non-local Data Interactions: Foundations and Applications
• Subjects: Natural sciences, medicine, IT, technology > IT, data processing > General, dictionaries; Social sciences, law, business > Media, communication > Communication science; COMPUTERS / General, Mathematical theory of computation, Data analysis: general, Data science and analysis: general