Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations.
Christian BeckFabian HornungMartin HutzenthalerArnulf JentzenThomas KrusePublished in: CoRR (2019)
Keyphrases
- partial differential equations
- solving partial differential equations
- taylor series
- numerical methods
- numerical solution
- difference equations
- finite difference
- image denoising
- numerical algorithms
- anisotropic diffusion
- level set
- ordinary differential equations
- image processing
- finite difference method
- numerical integration
- image enhancement
- differential equations
- fourth order
- energy functional
- curve evolution
- numerical scheme
- mathematical morphology
- approximation methods
- multiscale
- diffusion equation
- denoising
- mumford shah model
- nonlinear diffusion
- problems in image processing
- machine learning
- heat equation
- high order
- endpoints
- pattern recognition
- markov random field
- dynamical systems
- conservation laws
- variational methods
- similarity measure