Local bisection refinement for N-simplicial grids generated by reflection
SIAM Journal on Scientific Computing
An effective way to represent quadtrees
Communications of the ACM
Bottom-Up Construction and 2:1 Balance Refinement of Linear Octrees in Parallel
SIAM Journal on Scientific Computing
Multivariate Regression and Machine Learning with Sums of Separable Functions
SIAM Journal on Scientific Computing
Tensor Decompositions and Applications
SIAM Review
p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
SIAM Journal on Scientific Computing
Tree approximation of the long wave radiation parameterization in the NCAR CAM global climate model
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
This paper is concerned with scattered data approximation in high dimensions: Given a data set X@?R^d of N data points x^i along with values y^i@?R^d^^^', i=1,...,N, and viewing the y^i as values y^i=f(x^i) of some unknown function f, we wish to return for any query point x@?R^d an approximation f@?(x) to y=f(x). Here the spatial dimension d should be thought of as large. We emphasize that we do not seek a representation of f@? in terms of a fixed set of trial functions but define f@? through recovery schemes which are primarily designed to be fast and to deal efficiently with large data sets. For this purpose we propose new methods based on what we call sparse occupancy trees and piecewise linear schemes based on simplex subdivisions.