AI & ML
Flux-Matched Poisson Iteration for Generated Jacobian Equations: Local Convergence and Spectral Galerkin Approximation
arXiv cs.NA0 views
arXiv:2611.06153v1 Announce Type: new Abstract: We develop a flux-matched Poisson iteration for solving generated Jacobian equations with second boundary conditions. In each step, it solves a fixed shifted Poisson problem with a Neumann-type boundary condition. Near a smooth regular solution with positive $C^{1,1}$ densities, we prove that the iteration has local geometric convergence in $C^{2,\alpha}$ on smooth connected Riemannian domains. The iteration is then discretized using a spectral Galerkin method, with local convergence proved for the Fourier-Jacobi scheme on spherical caps. Optical numerical experiments support these estimates and demonstrate useful imaging performance beyond the local convergence theory.
Source：https://arxiv.org/abs/2611.06153PreviousReconstruction and well-posedness of an inverse coefficient problem for a diffusion equationNextOptimal Error Estimates With Polynomial Dependence on $\epsilon^{-1}$ for Mixed Finite Element Methods of the Cahn-Hilliard-Navier-Stokes System
Related posts
Changing the Time of Day in a Photo with a Text Prompt
0dev.to Tutorial
Soft vs Hard Subtitles: Which One Your Video Actually Needs
0dev.to Tutorial
The 5 Steps That Get Freelancers Paid (without sounding desperate)
0dev.to Career
What Are the Highest-Paying Machine Learning Jobs?
0dev.to Career
Two questions I added after readers replied
0dev.to Beginners
Government Workforce Training: How LMS Platforms Support Public Sector Learning and Development
0dev.to Beginners