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: J. Num. Math. (2020)
Keyphrases
- partial differential equations
- solving partial differential equations
- taylor series
- numerical methods
- numerical solution
- difference equations
- finite difference
- numerical integration
- ordinary differential equations
- image denoising
- finite difference method
- numerical algorithms
- image processing
- anisotropic diffusion
- level set
- image enhancement
- fourth order
- numerical scheme
- differential equations
- diffusion equation
- mathematical morphology
- multiscale
- approximation methods
- high order
- energy functional
- endpoints
- closed form
- curve evolution
- denoising
- heat equation
- boundary value problem
- nonlinear partial differential equations
- machine learning
- problems in image processing
- pattern recognition
- computational complexity
- image compression
- nonlinear diffusion
- active contours