Related papers: On the balanced truncation error bound and sign pa…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…
In this paper, we consider model order reduction for bilinear systems with non-zero initial conditions. We discuss choices of Gramians for both the homogeneous and the inhomogeneous parts of the system individually and prove how these…
The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain…
We propose a new method for controlling linear dynamical systems under adversarial disturbances and cost functions. Our algorithm achieves a running time that scales polylogarithmically with the inverse of the stability margin, improving…
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…
This work provides test error bounds for iterative fixed point methods on linear predictors -- specifically, stochastic and batch mirror descent (MD), and stochastic temporal difference learning (TD) -- with two core contributions: (a) a…
This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator…
To deploy machine learning-based algorithms for real-time applications with strict latency constraints, we consider an edge-computing setting where a subset of inputs are offloaded to the edge for processing by an accurate but…
Conditions are established under which the optimal control of processes having both absolutely continuous and singular (with respect to time) controls are equivalent to linear programs over a space of measures on the state and control…
Asymptotic approximations ($n \to \infty$) to the truncation errors $r_n = - \sum_{\nu=0}^{\infty} a_{\nu}$ of infinite series $\sum_{\nu=0}^{\infty} a_{\nu}$ for special functions are constructed by solving a system of linear equations.…
A novel procedure for the online identification of a class of discrete-time switched linear systems, which simultaneously estimates the parameters and switching manifolds of the systems, is proposed in this paper. Firstly, to estimate the…
The Neural Tangent Kernel (NTK) framework explains optimization in over-parameterized neural networks via approximately linearized dynamics, yielding exponential convergence guarantees. However, existing results are often overly pessimistic…
Linear TD($\lambda$) is one of the most fundamental reinforcement learning algorithms for policy evaluation. Previously, convergence rates are typically established under the assumption of linearly independent features, which does not hold…
The majority of existing probabilistic model checking case studies are based on well understood theoretical models and distributions. However, real-life probabilistic systems usually involve distribution parameters whose values are obtained…
This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables…
For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows to isolate the complicated asymptotic behavior of the system…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
In this article, we recover singularly-perturbed linear differential systems from their turning points and reduce the rank of the singularity in the parameter to its minimal integer value. Our treatment is Moser-based; that is to say it is…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…