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A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...
In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices.In the first part, we consider algorithms for building l ...
In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...
In this paper, we focus on a theory-practice gap for Adam and its variants (AMSgrad, AdamNC, etc.). In practice, these algorithms are used with a constant first-order moment parameter 1 (typically between 0:9 and 0:99). In theory, regret guarantees for onl ...
Data-driven modeling and feedback control play a vital role in several application areas ranging from robotics, control theory, manufacturing to management of assets, financial portfolios and supply chains. Many such problems in one way or another are rela ...
In this paper, we consider unilateral contact problem without friction between a rigid body and deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem. For the displacement, we use the pushforward ...
Two-dimensional (2D) flows can be controlled efficiently using spanwise "waviness," i.e., a control (e.g., wall blowing and suction or wall deformation) that is periodic in the spanwise direction. This study tackles the global linear stability of 2D flows ...
In this thesis, we consider commercial buildings with available heating, ventilation and air conditioning (HVAC) systems, and develop methods to assess and exploit their energy storage and production potential to collectively offer ancillary services to th ...
The significant progress that has been made in recent years both in hardware implementations and in numerical computing has rendered real-time optimization-based control a viable option when it comes to advanced industrial applications. At the same time, t ...
We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside prespecified safety sets at all times despite unknown disturbances. In this technical note, w ...