HODLR\(d\)D: a new black-box fast algorithm for \(N\)-body problems in \(d\)-dimensions with guaranteed error bounds. Applications to integral equations and support vector machines
From MaRDI portal
Publication:6126569
DOI10.1016/j.jcp.2024.112786arXiv2209.05819OpenAlexW4391179459WikidataQ129479301 ScholiaQ129479301MaRDI QIDQ6126569
Sivaram Ambikasaran, Ritesh Khan, Unnamed Author
Publication date: 9 April 2024
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2209.05819
Numerical linear algebra (65Fxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Kriging and spatial design accelerated by orders of magnitude: combining low-rank covariance approximations with FFT-techniques
- Fast construction of hierarchical matrix representation from matrix-vector multiplication
- A kernel-independent adaptive fast multipole algorithm in two and three dimensions
- A direct solver with \(O(N)\) complexity for integral equations on one-dimensional domains
- Recompression techniques for adaptive cross approximation
- The black-box fast multipole method
- Adaptive low-rank approximation of collocation matrices
- Construction and arithmetics of \(\mathcal H\)-matrices
- Introduction to hierarchical matrices with applications.
- Incomplete cross approximation in the mosaic-skeleton method
- Chebyshev interpolation for parametric option pricing
- Large-scale stochastic linear inversion using hierarchical matrices. Illustrated with an application to crosswell tomography in seismic imaging
- Hierarchical matrices based on a weak admissibility criterion
- A fast adaptive multipole algorithm in three dimensions
- Support-vector networks
- An \(\mathcal O(N\log N)\) fast direct solver for partial hierarchically semi-separable matrices. With application to radial basis function interpolation
- A wideband fast multipole method for the Helmholtz equation in three dimensions
- An \(O(N)\) direct solver for integral equations on the plane
- Statistical Regularization of Inverse Problems
- Fast algorithms for hierarchically semiseparable matrices
- Fast Directional Multilevel Algorithms for Oscillatory Kernels
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- A Fast Adaptive Multipole Algorithm for Particle Simulations
- On the Numerical Rank of Radial Basis Function Kernels in High Dimensions
- A Fast Direct Solver for Structured Linear Systems by Recursive Skeletonization
- Improved error bound for multivariate Chebyshev polynomial interpolation
- Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds
- Solving PDEs with radial basis functions
- High-dimensional integration: The quasi-Monte Carlo way
- Advanced Lectures on Machine Learning
- A Fast Solver for HSS Representations via Sparse Matrices
- Hierarchical adaptive low‐rank format with applications to discretized partial differential equations
- Randomized numerical linear algebra: Foundations and algorithms
- A fast algorithm for particle simulations
- HODLR2D: A New Class of Hierarchical Matrices