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This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are…
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
We consider the problem of sampling from a posterior distribution arising in Bayesian inverse problems in science, engineering, and imaging. Our method belongs to the family of independence Metropolis-Hastings (IMH) sampling algorithms,…
Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. The algorithm can achieve arbitrarily high-orders of convergence in terms of a…
The relationship between the operator approximation property and the strong operator approximation property has deep significance in the theory of operator algebras. The original definitions of Effros and Ruan, unlike the classical…
This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.
We give estimates for the approximation numbers of composition operators on the Hp spaces, 1 $\le$ p \textless{} $\infty$.
In this work, we highlight a connection between the incremental proximal method and stochastic filters. We begin by showing that the proximal operators coincide, and hence can be realized with, Bayes updates. We give the explicit form of…
There are two notions of approximate Birkhoff-James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on a normed space. A complete…
In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous…
This paper presents a novel method for recovering sparse vectors from linear models corrupted by Poisson noise. The contribution is twofold. First, an operator defined via the external division of two Bregman proximity operators is…
Computations on a manifold often involve constructing an operator on the tangent space and computing its inverse, which can be time-consuming in many applications. In order to reduce the computational costs and preserve the benign…
Approximate message passing (AMP) algorithms have shown great promise in sparse signal reconstruction due to their low computational requirements and fast convergence to an exact solution. Moreover, they provide a probabilistic framework…
Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization or incorporation of prior information about the underlying…
This is a continuation of our earlier paper \cite{PT3}. We consider here operator-valued functions (or infinite matrix functions) on the unit circle $\T$ and study the problem of approximation by bounded analytic operator functions. We…
Recently, various high-order methods have been developed to solve the convex optimization problem. The auxiliary problem of these methods shares the general form that is the same as the high-order proximal operator proposed by Nesterov. In…
The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a L_1 norm plus a pair-wise L_inf norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where…
Instance sparsification is well-known in the world of exact computation since it is very closely linked to the Exponential Time Hypothesis. In this paper, we extend the concept of sparsification in order to capture subexponential time…
We study the approximation numbers of weighted composition operators $f\mapsto w\cdot(f\circ\varphi)$ on the Hardy space $H^2$ on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers…