Related papers: Polynomial mapped bases: theory and applications
Data for several applications in diverse fields can be represented as multiple matrices that are linked across rows or columns. This is particularly common in molecular biomedical research, in which multiple molecular "omics" technologies…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the…
Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the…
The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary…
Motivated by several applications, we consider the problem of randomly rounding a fractional solution in a matroid (base) polytope to an integral one. We consider the pipage rounding technique and also present a new technique, randomized…
A blurring algorithm with linear time complexity can reduce the small-scale content of data observed at scattered locations in a spatially extended domain of arbitrary dimension. The method works by forming a Gaussian interpolant of the…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
Image resampling is a necessary component of any operation that changes the size of an image or its geometry. Methods tuned for natural image upsampling (roughly speaking, image enlargement) are analyzed and developed with a focus on their…
We consider quadrature formulas based on interpolation using the basis functions $1/(1+t_kx)$ $(k=1,2,3,\ldots)$ on $[-1,1]$, where $t_k$ are parameters on the interval $(-1,1)$. We investigate two types of quadratures: quadrature formulas…
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
We outline the super-resolution reconstruction problem posed as a maximization of probability. We then introduce an interpolation method based on polygonal pixel overlap, express it as a linear operator, and use it to improve…
This work is devoted to the study of integration with respect to binomial measures. We develop interpolatory quadrature rules and study their properties. Local error estimates for these rules are derived in a general framework.
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…
Geometric modeling of multivariate reliability polynomials is based on algebraic hypersurfaces, constant level sets, rulings etc. The solved basic problems are: (i) find the reliability polynomial using the Maple and Matlab software…
Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences,…
Multiple imputation is a highly recommended technique to deal with missing data, but the application to longitudinal datasets can be done in multiple ways. When a new wave of longitudinal data arrives, we can treat the combined data of…
We introduce a technique to decompose the scattered near field of two-dimensional arbitrary metaatoms into its multipole contributions. To this end we expand the scattered field upon plane wave illumination into cylindrical harmonics as…