Related papers: A splitting-based KPIK method for eddy current opt…

Solving fastest mixing Markov chain problem (i.e. finding transition probabilities on the edges to minimize the second largest eigenvalue modulus of the transition probability matrix) over networks with different topologies is one of the…

This paper presents the first results to combine two theoretically sound methods (spectral projection and multigrid methods) together to attack ill-conditioned linear systems. Our preliminary results show that the proposed algorithm applied…

We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize…

Exponential integrators are special time discretization methods where the traditional linear system solves used by implicit schemes are replaced with computing the action of matrix exponential-like functions on a vector. A very general…

Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To…

In this article, we derive a new, fast, and robust preconditioned iterative solution strategy for the all-at-once solution of optimal control problems with time-dependent PDEs as constraints, including the heat equation and the non-steady…

Quantum Krylov algorithms have emerged as a promising approach for ground-state energy estimation in the near-term quantum computing era. A major challenge, however, lies in their inherently substantial sampling cost, primarily due to the…

We derive error estimates for a linear-quadratic elliptic distributed optimal control problem with pointwise control constraints that can be applied to standard finite element methods and multiscale finite element methods.

This article is concerned with the nonconforming finite element method for distributed elliptic optimal control problems with pointwise constraints on the control and gradient of the state variable. We reduce the minimization problem into a…

The computation of sparse solutions of large-scale linear discrete ill-posed problems remains a computationally demanding task. A powerful framework in this context is the use of iteratively reweighted schemes, which are based on…

We consider a sketched implementation of the finite element method for elliptic partial differential equations on high-dimensional models. Motivated by applications in real-time simulation and prediction we propose an algorithm that…

In the present paper, we present some numerical methods for computing approximate solutions to some large differential linear matrix equations. In the first part of this work, we deal with differential generalized Sylvester matrix equations…

In this work, we propose a new method, termed as R-CORK, for the numerical solution of large-scale rational eigenvalue problems, which is based on a linearization and on a compact decomposition of the rational Krylov subspaces corresponding…

We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation…

We consider distributed optimization on undirected connected graphs. We propose a novel distributed conditional gradient method with (O(1/\sqrt{k})) convergence. Compared with existing methods, each iteration of our method uses both…

The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…

Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…

The efficient compression of kernel matrices, for instance the off-diagonal blocks of discretized integral equations, is a crucial step in many algorithms. In this paper, we study the application of Skeletonized Interpolation to construct…

Stabilizing autonomous linear time delay systems, particularly when addressing an unlimited number of pointwise and distributed delays (DDs) under dissipative constraints, poses a significant challenge. Existing solutions are often hindered…

We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…