Related papers: Computing polynomial conformal models for low-degr…
We consider the interpretation and the numerical construction of the inverse branches of $n$ factor Blaschke-products on the disk and show that these provide a generalization of the $n$-th root function. The inverse branches can be defined…
The notion of $p$-summing Bloch mapping from the complex unit open disc $\mathbb{D}$ into a complex Banach space $X$ is introduced for any $1\leq p\leq\infty$. It is shown that the linear space of such mappings, equipped with a natural…
Given a matrix $A$, the goal of the entrywise low-rank approximation problem is to find $\operatorname{argmin} \|A-B\|_p$ over all rank-$k$ matrices $B$, where $\| \cdot \|_p$ is the entrywise $\ell_p$ norm. When $p = 2$ this well-studied…
The notion of $p$-compact sets arises naturally from Grothendieck's characterization of compact sets as those contained in the convex hull of a norm null sequence. The definition, due to Sinha and Karn (2002), leads to the concepts of…
We present an algorithm to compute all Borcherds product paramodular cusp forms of a specified weight and level, describing its implementation in some detail and giving examples of its use.
We here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle: (i) Through the realization matrix of Schur stable systems. (ii) The Blaschke-Potapov product, which is then…
A method is developed to compute analytically fully symmetric cubature rules on the triangle by using symmetric polynomials to express the two kinds of invariance inherent in these rules. Rules of degree up to 15, some of them new and of…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
The o-minimal structure generated by the restricted Pfaffian functions, known as restricted sub-Pfaffian sets, admits a natural measure of complexity in terms of a format $\mathcal{F}$, recording information like the number of variables and…
Let $\Omega$ and $\Omega_{\fin}$ be the sets of all interpolating Blaschke products of type $G$ and of finite type $G$, respectively. Let $E$ and $E_{\fin}$ be the Douglas algebras generated by $H^\infty$ together with the complex…
Extending the results of Borichev--Golinskii--Kupin [2009], we obtain refined Blaschke-type necessary conditions on the zero distribution of analytic functions on the unit disk and on the complex plane with a cut along the positive…
Multiplication of polynomials is among key operations in computer algebra which plays important roles in developing techniques for other commonly used polynomial operations such as division, evaluation/interpolation, and factorization. In…
In this note, we examine how the BKP structure of the generating series of several models of maps on non-oriented surfaces can be used to obtain explicit and/or efficient recurrence formulas for their enumeration according to the genus and…
It is well known that the bounding curve of the central hyperbolic component of the Multibrot set in the parameter space of unicritical degree $d$ polynomials is an epicycloid with $d-1$ cusps. The interior of the epicycloid gives the…
We establish the existence of the Bernstein polynomial in one indeterminate $t$, and provide a method for its explicit computation. The Bernstein polynomial is associated with finitely generated modules over the Weyl algebra, known as…
We use the numerical conformal bootstrap to study six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories with flavor symmetry $\mathfrak{so}_{4k}$. We present evidence that minimal $(D_k, D_k)$ conformal matter saturates the…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
Sometimes only some digits of a numerical product or some terms of a polynomial or series product are required. Frequently these constitute the most significant or least significant part of the value, for example when computing initial…
We calculate the minimal surface bounded by four-sided figures whose projection on a plane is a rectangle, starting with the bilinear interpolation and using, for smoothness, the Chebyshev polynomial expansion in our discretized numerical…
In this paper we establish asymptotically best possible interpolation Lebesgue-type inequalities for $2\pi$-periodic functions $f$, which are representable as generalized Poisson integrals of the functions $\varphi$ from the space $L_p$,…