Related papers: Method for Verifying Solutions of Sparse Linear Sy…
In this paper, we extend the previous method for solving inverse problems for steady-state equations using the Generalized Collage Theorem by searching for an approximation that not only minimizes the collage error but also maximizes the…
This paper proposes a general framework to estimate coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification via rotational sparse approximation. In particular, we aim to identify a rotation matrix such that the…
In this paper, we describe a novel approach for checking safety specifications of a dynamical system with exogenous inputs over infinite time horizon that is guaranteed to terminate in finite time with a conclusive answer. We introduce the…
Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…
This paper suggests a nonparametric scheme to find the sparse solution of the underdetermined system of linear equations in the presence of unknown impulsive or non-Gaussian noise. This approach is robust against any variations of the noise…
This work considers methods for imposing sparsity in Bayesian regression with applications in nonlinear system identification. We first review automatic relevance determination (ARD) and analytically demonstrate the need to additional…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
Finding the solutions to a system of multivariate polynomial equations is a fundamental problem in mathematics and computer science. It involves evaluating the polynomials at many points, often chosen from a grid. In most current methods,…
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
Randomized matrix sparsification has proven to be a fruitful technique for producing faster algorithms in applications ranging from graph partitioning to semidefinite programming. In the decade or so of research into this technique, the…
In view of the KS-tensor complementarity problem, the sparse solution of this problem is studied. Due to the nonconvexity and noncontinuity of the l_0-norm, it is a NP hard problem to find the sparse solution of the KS-tensor…
Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially…
Runtime verification encompasses several lightweight techniques for checking whether a system's current execution satisfies a given specification. We focus on runtime verification for Linear Temporal Logic (LTL). Previous work describes…
We investigate the SPAI and PSAI preconditioning procedures and shed light on two important features of them: (i) For the large linear system $Ax=b$ with $A$ irregular sparse, i.e., with $A$ having $s$ relatively dense columns, SPAI may be…
In order to improve the performance of Least Mean Square (LMS) based system identification of sparse systems, a new adaptive algorithm is proposed which utilizes the sparsity property of such systems. A general approximating approach on…