Related papers: Low-rank approximation of Rippa method for RBF int…
We consider the problem of reconstructing 3D objects via meshfree interpolation methods. In this framework, we usually deal with large data sets and thus we develop an efficient local scheme via the well-known Partition of Unity (PU)…
The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…
We present a numerical framework for solving neural field equations on surfaces using Radial Basis Function (RBF) interpolation and quadrature. Neural field models describe the evolution of macroscopic brain activity, but modeling studies…
We have developed a parallel algorithm for radial basis function (RBF) interpolation that exhibits O(N) complexity,requires O(N) storage, and scales excellently up to a thousand processes. The algorithm uses a GMRES iterative solver with a…
In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms an orthogonal set and is adapted to the kernel seed function…
We present a new method for the solution of PDEs on manifolds $\mathbb{M} \subset \mathbb{R}^d$ of co-dimension one using stable scale-free radial basis function (RBF) interpolation. Our method involves augmenting polyharmonic spline (PHS)…
The quality of datasets is a critical issue in big data mining. More interesting things could be mined from datasets with higher quality. The existence of missing values in geographical data would worsen the quality of big datasets. To…
We investigate the problem of approximating the matrix function $f(A)$ by $r(A)$, with $f$ a Markov function, $r$ a rational interpolant of $f$, and $A$ a symmetric Toeplitz matrix. In a first step, we obtain a new upper bound for the…
We present a novel method for tuning the regularization hyper-parameter, $\lambda$, of a ridge regression that is faster to compute than leave-one-out cross-validation (LOOCV) while yielding estimates of the regression parameters of equal,…
We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set corresponding to the surface can be used for such…
We consider how some methods of uniform and nonuniform interpolation by translates of radial basis functions -- specifically the so-called general multiquadrics -- perform in the presence of certain types of noise. These techniques provide…
The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting…
We describe an efficient method for the approximation of functions using radial basis functions (RBFs), and extend this to a solver for boundary value problems on irregular domains. The method is based on RBFs with centers on a regular grid…
We present randUBV, a randomized algorithm for matrix sketching based on the block Lanzcos bidiagonalization process. Given a matrix $\bf{A}$, it produces a low-rank approximation of the form ${\bf UBV}^T$, where $\bf{U}$ and $\bf{V}$ have…
Leave-one-out cross-validation (LOOCV) can be particularly accurate among cross-validation (CV) variants for machine learning assessment tasks -- e.g., assessing methods' error or variability. But it is expensive to re-fit a model $N$ times…
Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address…
Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…
The low-rank alternating directions implicit (LR-ADI) iteration is a frequently employed method for efficiently computing low-rank approximate solutions of large-scale Lyapunov equations. In order to achieve a rapid error reduction, the…
Radial Basis Function Networks (RBFNs) are used primarily to solve curve-fitting problems and for non-linear system modeling. Several algorithms are known for the approximation of a non-linear curve from a sparse data set by means of RBFNs.…
Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…