Related papers: Tight Computationally Efficient Approximation of M…
Consensus problems for strings and sequences appear in numerous application contexts, ranging from bioinformatics over data mining to machine learning. Closing some gaps in the literature, we show that several fundamental problems in this…
This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for…
An upper bound on operator norms of compound matrices is presented, and special cases that involve the $\ell_1$, $\ell_2$ and $\ell_\infty$ norms are investigated. The results are then used to obtain bounds on products of the largest or…
Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
In the computational sciences, one must often estimate model parameters from data subject to noise and uncertainty, leading to inaccurate results. In order to improve the accuracy of models with noisy parameters, we consider the problem of…
We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex…
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…
The present paper provides a comprehensive study of de-noising properties of frames and, in particular, tight frames, which constitute one of the most popular tools in contemporary signal processing. The objective of the paper is to bridge…
A central problem in data streams is to characterize which functions of an underlying frequency vector can be approximated efficiently. Recently there has been considerable effort in extending this problem to that of estimating functions of…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
When facing time-variant problems in analog computing, the desirable RNN design requires finite-time convergence and robustness with respect to various types of uncertainties, due to the time-variant nature and difficulties in…
We consider the problem of estimating the spectral norm of a matrix using only matrix-vector products. We propose a new Counterbalance estimator that provides upper bounds on the norm and derive probabilistic guarantees on its…
We show that computing even very coarse approximations of critical points is intractable for simple classes of nonconvex functions. More concretely, we prove that if there exists a polynomial-time algorithm that takes as input a polynomial…
Safety-critical navigation applications require that estimation errors be reliably quantified and bounded. This can be challenging for linear dynamic systems if the process noise or measurement errors have uncertain time correlation. In…
The matrix $p \rightarrow q$ norm is a fundamental quantity appearing in a variety of areas of mathematics. This quantity is known to be efficiently computable in only a few special cases. The best known algorithms for approximately…
The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP.…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…