Related papers: Complexity of Creative Telescoping for Bivariate R…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
Leveraging a general framework adapted from symbolic integration, a unified reduction-based algorithm for computing telescopers of minimal order for hypergeometric and q-hypergeometric terms has been recently developed. In this paper, we…
We develop an underlying relationship between the theory of rational approximations and that of isomonodromic deformations. We show that a certain duality in Hermite's two approximation problems for functions leads to the Schlesinger…
The aim of this work is to show how symbolic computation can be used to perform multivariate Lagrange, Hermite and Birkhoff interpolation and help us to build more realistic interpolating functions. After a theoretical introduction in which…
We propose a new lifting and recombination scheme for rational bivariate polynomial factorization that takes advantage of the Newton polytope geometry. We obtain a deterministic algorithm that can be seen as a sparse version of an algorithm…
Zaremba's Conjecture concerns the formation of continued fractions with partial quotients restricted to a given alphabet. In order to answer the numerous questions that arrive from this conjecture, it is best to consider a semi-group, often…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
We present a rigorous mathematical solution to photometric redshift estimation and the more general inversion problem. The challenge we address is to meaningfully constrain unknown properties of astronomical sources based on given…
This paper proposes ideas to speed up the process of creative telescoping, particularly when the telescoper is reducible. One can interpret telescoping as computing an annihilator $L \in D$ for an element $m$ in a $D$-module $M$. The main…
This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…
Consider a rational map from a projective space to a product of projective spaces, induced by a collection of linear projections. Motivated by the the theory of limit linear series and Abel-Jacobi maps, we study the basic properties of the…
We report major advances in the research program initiated in "Moment-Based Evidence for Simple Rational-Valued Hilbert-Schmidt Generic 2 x 2 Separability Probabilities" (J. Phys. A, 45, 095305 [2012]). A highly succinct separability…
We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We give a new complexity bound for calculating the complex dimension of an algebraic set. Our algorithm is completely deterministic and approaches the best recent randomized complexity bounds. We also present some new, significantly sharper…
We present a rational version of the classical Landen transformation for elliptic integrals. This is employed to obtain explicit closed-form expressions for a large class of integrals of even rational functions and to develop an algorithm…
Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…
The problem of minimization of the sum of two convex functions has various theoretical and real-world applications. One of the popular methods for solving this problem is the proximal gradient method (proximal forward-backward algorithm). A…
We first consider the problem of approximating a few eigenvalues of a rational matrix-valued function closest to a prescribed target. It is assumed that the proper rational part of the rational matrix-valued function is expressed in the…