Related papers: Frame approximation with bounded coefficients

A (unit norm) frame is scalable if its vectors can be rescaled so as to result into a tight frame. Tight frames can be considered optimally conditioned because the condition number of their frame operators is unity. In this paper we…

In this paper we consider from two different aspects the proximal alternating direction method of multipliers (ADMM) in Hilbert spaces. We first consider the application of the proximal ADMM to solve well-posed linearly constrained…

In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…

Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This…

Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters…

In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…

We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…

In paper a new definition of reduced Pade approximant and algorithm for its computing is proposed. Our approach is based on the investigation of the kernel structure of the Toeplitz matrix. It is shown that the reduced Pade approximant…

Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…

Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We…

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…

We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. We present a method to determine the maximum robustness of a frame. We present results on tight subframes and…

We consider stochastic approximations which arise from such applications as data communications and image processing. We demonstrate why constraints are needed in a stochastic approximation and how a constrained approximation can be…

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

Frame theory provides a robust method for recovering vectors in a Hilbert space from inner product data, though the associated decomposition formula can be computationally demanding. We relax the frame condition by studying sequences that…

A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and…

Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…

A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that realizes a holistic understanding of a fully commutative…

Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…