Differential Equations and Variational Methods on Graphs by Yves Van Gennip
The burgeoning field of differential equations on graphs has experienced significant growth in the past decade, propelled by the use of variational methods in imaging and by its applications in machine learning. This text provides a detailed overview of the subject, serving as a reference for researchers and as an introduction for graduate students wishing to get up to speed. The authors look through the lens of variational calculus and differential equations, with a particular focus on graph-Laplacian-based models and the graph Ginzburg-Landau functional. They explore the diverse applications, numerical challenges, and theoretical foundations of these models. A meticulously curated bibliography comprising approximately 800 references helps to contextualise this work within the broader academic landscape. While primarily a review, this text also incorporates some original research, extending or refining existing results and methods.-
Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
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Kernel-Based Methods
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Infinite-Dimensional Spectral Computations
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Numerical Bifurcation Analysis of Maps
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Collocation Methods for Volterra Integral and Related Functional Differential Equations
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The Mathematical Foundations of Mixing
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Partial Differential Equation Methods for Image Inpainting
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Topology for Computing
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High-Order Methods for Incompressible Fluid Flow
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Generalized Riemann Problems in Computational Fluid Dynamics
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Multivariate Approximation
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Iterative Krylov Methods for Large Linear Systems
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Dynamical Systems and Numerical Analysis
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Volterra Integral Equations
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Scattered Data Approximation
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Greedy Approximation
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A Practical Guide to the Invariant Calculus
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Orthogonal Rational Functions
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Geometry and Topology for Mesh Generation
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Curve and Surface Reconstruction
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Algebraic Geometry and Statistical Learning Theory
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The Numerical Solution of Integral Equations of the Second Kind
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Radial Basis Functions
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A Practical Guide to Pseudospectral Methods
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Spectral Methods for Time-Dependent Problems
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Multiscale Methods for Fredholm Integral Equations
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Minimal Cubature Rules
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High-Accuracy Finite Difference Methods
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An Introduction to Immersed Boundary Methods
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Modern Computer Arithmetic
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Matrix Preconditioning Techniques and Applications
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Geometry of the Phase Retrieval Problem
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Quasi-Interpolation
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The Christoffel–Darboux Kernel for Data Analysis
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Difference Equations by Differential Equation Methods
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Learning Theory
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Schwarz-Christoffel Mapping
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Simulating Hamiltonian Dynamics
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Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations
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Discrete Variational Problems with Interfaces
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Spaces of Measures and their Applications to Structured Population Models
Yves van Gennip is Associate Professor in the Delft Institute of Applied Mathematics (DIAM) at Delft University of Technology. Jeremy Budd is Assistant Professor of Mathematics and its Applications at the University of Birmingham.
| SKU | Unavailable |
| ISBN 13 | 9781009556682 |
| ISBN 10 | 1009556681 |
| Title | Differential Equations and Variational Methods on Graphs |
| Author | Yves Van Gennip |
| Series | Cambridge Monographs On Applied And Computational Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2025-11-30 |
| Number of pages | 389 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |