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Low rank tensor completion is a highly ill-posed inverse problem, particularly when the data model is not accurate, and some sort of regularization is required in order to solve it. In this article we focus on the calibration of the data…

In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first…

The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…

We give a spectral algorithm for decomposing overcomplete order-4 tensors, so long as their components satisfy an algebraic non-degeneracy condition that holds for nearly all (all but an algebraic set of measure $0$) tensors over…

In many supervised learning applications, the response consists of both continuous and binary outcomes. Studies have shown that jointly modeling such mixed-type responses can substantially improve predictive performance compared to separate…

We present the bilateral solver, a novel algorithm for edge-aware smoothing that combines the flexibility and speed of simple filtering approaches with the accuracy of domain-specific optimization algorithms. Our technique is capable of…

In this work, we consider the problem of blind source separation (BSS) by departing from the usual linear model and focusing on the linear-quadratic (LQ) model. We propose two provably robust and computationally tractable algorithms to…

Representation-based multi-task learning (MTL) improves efficiency by learning a shared structure across tasks, but its practical application is often hindered by contamination, outliers, or adversarial tasks. Most existing methods and…

Numerical exceptions, which may be caused by overflow, operations like division by 0 or sqrt(-1), or convergence failures, are unavoidable in many cases, in particular when software is used on unforeseen and difficult inputs. As more…

In computational fluid dynamics, the demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational advances in individual components of future solvers. At the…

Multi-task learning enhances model generalization by jointly learning from related tasks. This paper focuses on the $\ell_{1,\infty}$-norm constrained multi-task learning problem, which promotes a shared feature representation while…

We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle…

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

The method of regularised stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard…

We present a high-performance solver for dense skew-symmetric matrix eigenvalue problems. Our work is motivated by applications in computational quantum physics, where one solution approach to solve the so-called Bethe-Salpeter equation…

We present an efficient robust value iteration for \texttt{s}-rectangular robust Markov Decision Processes (MDPs) with a time complexity comparable to standard (non-robust) MDPs which is significantly faster than any existing method. We do…

Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of characteristic equation and the argument principle, an algorithm is generated which is shown to outperform…

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…

This paper introduces a new deep learning approach to approximately solve the Covering Salesman Problem (CSP). In this approach, given the city locations of a CSP as input, a deep neural network model is designed to directly output the…

In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…