Related papers: Improved Approximations of Hedges' g*
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…
The aim of this paper is to apply an original computation method due to Malesevic and Makragic [5] to the problem of approximating some trigonometric functions. Inequalities of Wilker-Cusa-Huygens are discussed, but the method can be…
Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…
The purpose of this paper is to show how Gelfand's formula and balancing can be used to improve the upper and lower bounds of the spectrum of a companion matrix associated with a given real or complex polynomial. Examples and other related…
We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to multiple polynomial inputs. For a given pair of polynomials and a degree, our algorithm…
We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to polynomials with the complex coefficients. For a given pair of polynomials and a…
Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including…
We study the problem of approximating an unknown function $f:\mathbb{R}\to\mathbb{R}$ by a degree-$d$ polynomial using as few function evaluations as possible, where error is measured with respect to a probability distribution $\mu$.…
We introduce Generalized Integrated Gradients (GIG), a formal extension of the Integrated Gradients (IG) (Sundararajan et al., 2017) method for attributing credit to the input variables of a predictive model. GIG improves IG by explaining a…
A multiplicative $\alpha$-spanner $H$ is a subgraph of $G=(V,E)$ with the same vertices and fewer edges that preserves distances up to the factor $\alpha$, i.e., $d_H(u,v)\leq\alpha\cdot d_G(u,v)$ for all vertices $u$, $v$. While many…
A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…
We present an iterative algorithm for calculating approximate greatest common divisor (GCD) of univariate polynomials with the real or the complex coefficients. For a given pair of polynomials and a degree, our algorithm finds a pair of…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
This paper describes a method for estimating conditional probability distributions over the parses of ``unification-based'' grammars which can utilize auxiliary distributions that are estimated by other means. We show how this can be used…
In practice, there often exist unobserved variables, also termed hidden variables, associated with both the response and covariates. Existing works in the literature mostly focus on linear regression with hidden variables. However, when the…
When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…
We present some properties of measures (q-Gaussian) that orthogonalize the set of q-Hermite polynomials. We also present an algorithm for simulating i.i.d. sequences of random variables having q-Gaussian distribution.
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…