GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
Updating the inverse of a matrix
SIAM Review
SIAM Journal on Scientific and Statistical Computing
Preconditioning for boundary integral equations
SIAM Journal on Matrix Analysis and Applications
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
The fast multipole method: numerical implementation
Journal of Computational Physics
An Analysis of Sparse Approximate Inverse Preconditioners for Boundary Integral Equations
SIAM Journal on Matrix Analysis and Applications
The Fast Multipole Method I: Error Analysis and Asymptotic Complexity
SIAM Journal on Numerical Analysis
Radial Basis Functions
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Journal of Computational Physics
Fast monte-carlo algorithms for finding low-rank approximations
Journal of the ACM (JACM)
On the Compression of Low Rank Matrices
SIAM Journal on Scientific Computing
A fast direct solver for boundary integral equations in two dimensions
Journal of Computational Physics
Some Fast Algorithms for Sequentially Semiseparable Representations
SIAM Journal on Matrix Analysis and Applications
A Fast $ULV$ Decomposition Solver for Hierarchically Semiseparable Representations
SIAM Journal on Matrix Analysis and Applications
Mesh deformation based on radial basis function interpolation
Computers and Structures
Fast Radial Basis Function Interpolation via Preconditioned Krylov Iteration
SIAM Journal on Scientific Computing
A Fast Direct Solver for a Class of Elliptic Partial Differential Equations
Journal of Scientific Computing
The black-box fast multipole method
Journal of Computational Physics
Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation
Journal of Computational Physics
A fast direct solver for elliptic problems on general meshes in 2D
Journal of Computational Physics
The effect of the nugget on Gaussian process emulators of computer models
Computational Statistics & Data Analysis
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This article describes a fast direct solver (i.e., not iterative) for partial hierarchically semi-separable systems. This solver requires a storage of $$\mathcal O (N \log N)$$O(NlogN) and has a computational complexity of $$\mathcal O (N \log N)$$O(NlogN) arithmetic operations. The numerical benchmarks presented illustrate the method in the context of interpolation using radial basis functions. The key ingredients behind this fast solver are recursion, efficient low rank factorization using Chebyshev interpolation, and the Sherman---Morrison---Woodbury formula. The algorithm and the analysis are worked out in detail. The performance of the algorithm is illustrated for a variety of radial basis functions and target accuracies.