Related papers: The Gauss quadrature for general linear functional…
This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…
While dealing with matching shapes to their parts, we often apply a tool known as functional maps. The idea is to translate the shape matching problem into "convenient" spaces by which matching is performed algebraically by solving a least…
We propose a totally functional view of geometric matrix completion problem. Differently from existing work, we propose a novel regularization inspired from the functional map literature that is more interpretable and theoretically sound.…
We analyze randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation. The algorithms studied include the kernel polynomial method and stochastic Lanczos quadrature, two widely used methods for these tasks. Our…
The Cauchy problem for the Gross--Pitaevsky equation with quadratic nonlocal nonlinearity is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear…
We introduce a new type of quadrature, known as approximate Gaussian quadrature (AGQ) rules using {\epsilon}-quasiorthogonality, for the approximation of integrals of the form \int f(x)d \alpha(x). The measure {\alpha}(\cdot) can be…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex…
Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
Highly oscillatory integrals of composite type arise in electronic engineering and their calculations is a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is…
In this paper, we analyze some theoretical properties of the problem of minimizing a quadratic function with a cubic regularization term, arising in many methods for unconstrained and constrained optimization that have been proposed in the…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
We present a generic approach that allows us to develop a fully polynomial-time approximation scheme (FTPAS) for minimizing nonlinear functions over the integer points in a rational polyhedron in fixed dimension. The approach combines the…
The paper presents partial-realization theory and realization algorithms for linear switched systems. Linear switched systems are a particular subclass of hybrid systems. We formulate a notion of a partial realization and we present…
We study numerical integration of Lipschitz functionals on a Banach space by means of deterministic and randomized (Monte Carlo) algorithms. This quadrature problem is shown to be closely related to the problem of quantization of the…
We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy lower bounds when the initial problem formulation exhibits a high degree of symmetry. Our main technical theorem allows us to reduce the study of the positive…