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This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…

Systems and Control · Computer Science 2018-04-18 Zuogong Yue , Johan Thunberg , Lennart Ljung , Jorge Goncalves

We consider approximating solutions to parameterized linear systems of the form $A(\mu_1,\mu_2) x(\mu_1,\mu_2) = b$. Here the matrix $A(\mu_1,\mu_2) \in \mathbb{R}^{n \times n}$ is nonsingular, large, and sparse and depends nonlinearly on…

Numerical Analysis · Mathematics 2025-02-27 Siobhán Correnty , Melina A. Freitag , Kirk M. Soodhalter

Solving multiple parametrised related systems is an essential component of many numerical tasks, and learning from the already solved systems will make this process faster. In this work, we propose a novel probabilistic linear solver over…

Machine Learning · Statistics 2025-08-21 Disha Hegde , Jon Cockayne

Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…

Data Structures and Algorithms · Computer Science 2020-08-07 Nai-Hui Chia , Tongyang Li , Han-Hsuan Lin , Chunhao Wang

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…

Machine Learning · Computer Science 2019-02-05 Max Simchowitz , Ross Boczar , Benjamin Recht

Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation…

Data Structures and Algorithms · Computer Science 2014-09-15 Faisal N. Abu-Khzam , Cristina Bazgan , Morgan Chopin , Henning Fernau

We consider a family of linear systems $A_\mu \alpha=C$ with system matrix $A_\mu$ depending on a parameter $\mu$ and for simplicity parameter-independent right-hand side $C$. These linear systems typically result from the…

Numerical Analysis · Mathematics 2013-07-17 Fabien Casenave , Alexandre Ern , Tony Lelièvre , Guillaume Sylvand

We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…

Optimization and Control · Mathematics 2013-08-12 Péter Koltai , Alexander Volf

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

Numerical Analysis · Mathematics 2021-10-22 Peter Sentz , Kristian Beckwith , Eric C. Cyr , Luke N. Olson , Ravi Patel

The description of complex physical phenomena often involves sophisticated models that rely on a large number of parameters, with many dimensions and scales. One practical way to simplify that kind of models is to discard some of the…

Soft Condensed Matter · Physics 2025-11-11 Simone Rusconi , Christina Schenk , Razvan Ceuca , Arghir Zarnescu , Elena Akhmatskaya

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…

This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.

Spectral Theory · Mathematics 2025-10-20 B. M. Brown , M. S. P. Eastham , D. K. R. McCormack

We present a polynomial-time algorithm that obtains a set of Asymptotic Linear Programs (ALPs) from a given linear system S, such that one of these ALPs admits a feasible solution if and only if S admits a feasible solution. We also show…

Computational Complexity · Computer Science 2012-06-20 Deepak Ponvel Chermakani

This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…

Methodology · Statistics 2021-09-13 Jason Xu , Kenneth Lange

The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…

Optimization and Control · Mathematics 2021-10-13 Alberto Padoan

In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…

Numerical Analysis · Mathematics 2024-08-29 Hendrik Kleikamp , Lukas Renelt

We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial,…

Machine Learning · Computer Science 2023-09-26 Nikolaos P. Bakas

This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…

Systems and Control · Electrical Eng. & Systems 2021-12-07 Biqiang Mu , Tianshi Chen , Changming Cheng , Er-Wei Bai

In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…

Optimization and Control · Mathematics 2015-03-05 Zahra Roshan Zamir , Nadezda Sukhorukova