Related papers: Moving least squares via orthogonal polynomials
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…
We present computational methods for constructing orthogonal/orthonormal polynomials over arbitrary polygonal domains in $\mathbb{R}^2$ using bivariate spline functions. Leveraging a mature MATLAB implementation which generates spline…
Data approximation is essential in fields such as geometric design, numerical PDEs, and curve modeling. Moving Least Squares (MLS) is a widely used method for data fitting; however, its accuracy degrades in the presence of discontinuities,…
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…
We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields.…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
To find the least squares solution of a very large and inconsistent system of equations, one can employ the extended Kaczmarz algorithm. This method simultaneously removes the error term, such that a consistent system is asymptotically…
Low discrepancy point sets have been widely used as a tool to approximate continuous objects by discrete ones in numerical processes, for example in numerical integration. Following a century of research on the topic, it is still unclear…
In this article the error estimation of the moving least squares approximation is provided for functions in fractional order Sobolev spaces. The analysis presented in this paper extends the previous estimations and explains some unnoticed…
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…
In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonotone r-by-s matrices. These algorithms can be used, for…
Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained…
A new method of composition orthogonality is introduced. It is applied to generate new sequences of orthogonal polynomials and functions. In particular, classical orthogonal polynomials are interpreted in the sense of composition…
This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much…
We present an efficient method for image segmentation in the presence of strong inhomogeneities. The approach can be interpreted as a two-level clustering procedure: pixels are first grouped into superpixels via a linear least-squares…
Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
The study of several naturally arising "nearest neighbours" random walks benefits from the study of the associated orthogonal polynomials and their orthogonality measure. I consider extensions of this approach to a larger class of random…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
The objective of the matrix selection problem is to select a submatrix $A_{S}\in \mathbb{R}^{n\times k}$ from $A\in \mathbb{R}^{n\times m}$ such that its minimum singular value is maximized. In this paper, we employ the interlacing…