Graph-theoretic algorithms for Kolmogorov operators: approximating solutions and their gradients in elliptic and parabolic problems on manifolds

DOI10.1007/s10092-022-00495-0OpenAlexW3157279470MaRDI QIDQ2111184

Andrew D. Davis, Dimitrios Giannakis

Publication date: 28 December 2022

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.15124

zbMATH Keywords

kernel methodsvector fieldsgraph LaplacianKolmogorov operators

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Algorithms for approximation of functions (65D15)

Related Items (1)

Particle-Continuum Multiscale Modeling of Sea Ice Floes

Uses Software

• NLopt
• nanoflann
• GitHub

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Refinements to nearest-neighbor searching in k-dimensional trees
• Variable bandwidth diffusion kernels
• Variable kernel density estimation
• Accounting for boundary effects in nearest-neighbor searching
• Geometric structures arising from kernel density estimation on Riemannian manifolds
• A randomized approximate nearest neighbors algorithm
• Error estimates for spectral convergence of the graph Laplacian on random geometric graphs toward the Laplace-Beltrami operator
• Data-driven spectral decomposition and forecasting of ergodic dynamical systems
• Kernel density estimation on Riemannian manifolds
• Diffusion maps
• From graph to manifold Laplacian: the convergence rate
• An optimal algorithm for approximate nearest neighbor searching fixed dimensions
• Uncertainty Quantification in Graph-Based Classification of High Dimensional Data
• Multidimensional binary search trees used for associative searching
• An Algorithm for Finding Best Matches in Logarithmic Expected Time
• On Locally Adaptive Density Estimation
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Analysis and Geometry of Markov Diffusion Operators
• Spectral Exterior Calculus
• Graph Laplacian Tomography From Unknown Random Projections
• On Estimation of a Probability Density Function and Mode

This page was built for publication: Graph-theoretic algorithms for Kolmogorov operators: approximating solutions and their gradients in elliptic and parabolic problems on manifolds