Related papers: Approximating the Real Structured Stability Radius…
Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…
In this paper we consider parallel implementations of approximate multiplication of large matrices with exponential decay of elements. Such matrices arise in computations related to electronic structure calculations and some other fields of…
The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…
State space subspace algorithms for input-output systems have been widely applied but also have a reasonably well-developedasymptotic theory dealing with consistency. However, guaranteeing the stability of the estimated system matrix is a…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
Consider a matrix polynomial $P \left( \lambda \right)= A_0 + \lambda A_1 + \ldots + \lambda^d A_d$, with $A_0,\ldots, A_d$ complex (or real) matrices with a certain structure. In this paper we discuss an iterative method to numerically…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
A novel algorithm for real-time modal identification in linear vibrating systems with complex modes is introduced, utilizing a combination of first order eigen-perturbation and second order separation techniques. In practical settings,…
The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The approximation problem in Frobenius norm admits a well-known…
Perturbation theory is developed to analyze the impact of noise on data and has been an essential part of numerical analysis. Recently, it has played an important role in designing and analyzing matrix algorithms. One of the most useful…
Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
In practical applications, quantum systems are inevitably subject to significant uncertainties, including unknown initial states, imprecise physical parameters, and unmodeled environmental noise, all of which pose major challenges to robust…
We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the…
In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in…
We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various…
This paper introduces a new proximal stochastic gradient method with variance reduction and stabilization for minimizing the sum of a convex stochastic function and a group sparsity-inducing regularization function. Since the method may be…
We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…