Related papers: An Optimal Ansatz Space for Moving Least Squares A…
There is a need to improve the capability of the adaptive filtering algorithm against Gaussian or multiple types of non-Gaussian noises, time-varying system, and systems with low SNR. In this paper, we propose an optimized least mean…
This paper presents a stochastic approximation proximal subgradient (SAPS) method for stochastic convex-concave minimax optimization. By accessing unbiased and variance bounded approximate subgradients, we show that this algorithm exhibits…
The approximate nearest neighbor problem ($\epsilon$-ANN) in high dimensional Euclidean space has been mainly addressed by Locality Sensitive Hashing (LSH), which has polynomial dependence in the dimension, sublinear query time, but…
We study theoretical and computational aspects of the least squares fit (LSF) of circles and circular arcs. First we discuss the existence and uniqueness of LSF and various parametrization schemes. Then we evaluate several popular circle…
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…
The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers,…
We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…
We have employed Particle Swarm Optimization to address a stochastic variant of the Smallest Enclosing Sphere estimation problem. An efficient algorithm has been developed to ascertain the optimal center and radius of a sphere encompassing…
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…
Functional partial least squares (FPLS) is commonly used for fitting scalar-on-function regression models. For the sake of accuracy, FPLS demands that each realization of the functional predictor is recorded as densely as possible over the…
In this paper, Sphere Decoding (SD) algorithms for Spatial Modulation (SM) are developed to reduce the computational complexity of Maximum-Likelihood (ML) detectors. Two SDs specifically designed for SM are proposed and analysed in terms of…
Witsenhausen's problem asks for the maximum fraction $\alpha_n$ of the $n$-dimensional unit sphere that can be covered by a measurable set containing no pairs of orthogonal points. The best upper bounds for $\alpha_n$ are given by…
We address an algorithm for the least squares fitting of a subset of the eigenvalues of an unknown Hermitian matrix lying an an affine subspace, called the Lift and Projection (LP) method, due to Chen and Chu (SIAM Journal on Numerical…
Extremum seeking (ES) optimization approach has been very popular due to its non-model based analysis and implementation. This approach has been mostly used with gradient based search algorithms. Since least squares (LS) algorithms are…
In this work, we apply two meshless methods for the numerical solution of the time-dependent transport equation defined on the sphere in spherical coordinates. The first technique, which was introduced by Mirzaei (BIT Numerical Mathematics,…
The purpose of this paper is to establish L^p error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular,…
In this paper we consider $L_{\overline{p}, \overline\alpha, \overline{\tau}}^{*}(\mathbb{T}^{m})$ anisotropic Lorentz-Zyg\-mu\-nd space $ 2\pi$ of periodic functions of $m$ variables and Nikol'skii--Besov's class $S_{\overline{p},…
This paper considers filtered polynomial approximations on the unit sphere $\mathbb{S}^d\subset \mathbb{R}^{d+1}$, obtained by truncating smoothly the Fourier series of an integrable function $f$ with the help of a "filter" $h$, which is a…
The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…
This paper presents a method for the approximation of harmonic potentials that combines downward continuation of globally available data on a sphere $\Omega_R$ of radius $R$ (e.g., a satellite's orbit) with locally available data on a…