相关论文: Finite-rank approximation of affine processes on p…
We revisit affine diffusion processes on general and on the canonical state space in particular. A detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions…
It is well known that the affine matrix rank minimization problem is NP-hard and all known algorithms for exactly solving it are doubly exponential in theory and in practice due to the combinational nature of the rank function. In this…
In affine models, both the martingale property of stochastic exponentials and non-explosion of affine processes is characterized in terms of minimality of solutions to a system of generalized Riccati differential equations. This is the…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…
We present two parallel optimization algorithms for a convex function $f$. The first algorithm optimizes over linear inequality constraints in a Hilbert space, $\mathbb H$, and the second over a non convex polyhedron in $\mathbb R^n$. The…
This work develops a functional-analytic framework based on the transfinite iteration of a self-adjoint operator. Beginning with a densely defined self-adjoint operator $A$ on a Hilbert space $H$, a spectral-transform functor $\Phi$ is…
This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physics. In a wavelet-Galerkin framework, we formulate learning…
In this note we continue our investigations of the representation theoretic aspects of reflection positivity, also called Osterwalder--Schrader positivity. We explain how this concept relates to affine isometric actions on real Hilbert…
In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…
In this work, we introduce new approximation operators for univariate set-valued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new…
Low-rank approximation of a matrix function, $f(A)$, is an important task in computational mathematics. Most methods require direct access to $f(A)$, which is often considerably more expensive than accessing $A$. Persson and Kressner (SIMAX…
Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various…
In this paper we study variational inequalities in a real Hilbert space, which are governed by a strongly monotone and Lipschitz continuous operator $F$ over a closed and convex set $C$. We assume that the set $C$ can be outerly…
Post-processing techniques are essential tools for enhancing the accuracy of finite element approximations and achieving superconvergence. Among these, recovery techniques stand out as vital methods, playing significant roles in both…
We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed…
This manuscript proposes a class of fractional stochastic integro-differential equation (FSIDE) with non-instantaneous impulses in an arbitrary separable Hilbert space. We use a projection scheme of increasing sequence of finite dimensional…
We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic…
We study a decentralized variant of stochastic approximation, a data-driven approach for finding the root of an operator under noisy measurements. A network of agents, each with its own operator and data observations, cooperatively find the…
In this paper, we develop and study algorithms for approximately solving the linear algebraic systems: $\mathcal{A}_h^\alpha u_h = f_h$, $ 0< \alpha <1$, for $u_h, f_h \in V_h$ with $V_h$ a finite element approximation space. Such problems…