Related papers: Approximation by analytic operator functions. Fact…

We investigate the existence of approximation algorithms for maximization of submodular functions, that run in fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function $v: 2^X \to \mathbb{R}$ the goal is to…

Given a matrix-valued function $\mathcal{F}(\lambda)=\sum_{i=1}^d f_i(\lambda) A_i$, with complex matrices $A_i$ and $f_i(\lambda)$ entire functions for $i=1,\ldots,d$, we discuss a method for the numerical approximation of the distance to…

computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…

Functionally constrained stochastic optimization problems, where neither the objective function nor the constraint functions are analytically available, arise frequently in machine learning applications. In this work, assuming we only have…

This article explores the extension of the classical approximation property and its variants to the nonlinear framework of Lipschitz operator theory. Building on Grothendieck's tensor product methodology, we characterize the Lipschitz…

Let $T:Y\to X$ be a bounded linear operator between two normed spaces. We characterize compactness of $T$ in terms of differentiability of the Lipschitz functions defined on $X$ with values in another normed space $Z$. Furthermore, using a…

We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

Finite (word) state transducers extend finite state automata by defining a binary relation over finite words, called rational relation. If the rational relation is the graph of a function, this function is said to be rational. The class of…

The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…

This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a…

In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of…

We consider a minimal realization of a rational matrix functions. We perturb the polynomial part and one of the constant matrices from the realization part. We derive explicit computable expressions of backward errors of approximate…

In this paper we characterize the approximation schemes that satisfy Shapiro's theorem and we use this result for several classical approximation processes. In particular, we study approximation of operators by finite rank operators and…

The polar factor of a bounded operator acting on a Hilbert space is the unique partial isometry arising in the polar decomposition. It is well known that the polar factor might not be a best approximant to its associated operator in the set…

This is a study of inner-outer factorization for analytic matrix-valued functions focusing on representations of the factors in terms of multiplicative integrals. Included is a brief introduction to the theory of multiplicative integrals…

We construct operators which factorize the transfer function associated with a non-self-adjoint 2x2 operator matrix whose diagonal entries can have overlapping spectra and whose off-diagonal entries are unbounded operators.

We consider the problem of minimizing the composition of a nonsmooth function with a smooth mapping in the case where the proximity operator of the nonsmooth function can be explicitly computed. We first show that this proximity operator…

In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].

We consider the problem of finding the best harmonic or analytic approximant to a given function. We discuss when the best approximant is unique, and what regularity properties the best approximant inherits from the original function. All…