In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...
In this thesis work, we propose to exploit an innovative micro/nano-fabrication process, based on controlled fluid instabilities of a thin viscous film of chalcogenide glass. Amorphous selenium and arsenic triselenide were used in this thesis work, and com ...
We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...
Humans are chronically exposed to airborne microplastics (MPs) by inhalation. Various types of polymer particles have been detected in lung samples, which could pose a threat to human health. Inhalation toxicological studies are crucial for assessing the e ...
Volume electron microscopy is the method of choice for the in situ interrogation of cellular ultrastructure at the nanometer scale, and with the increase in large raw image datasets generated, improving computational strategies for image segmentation and s ...
This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...
Deep learning has revolutionized the field of computer vision, a success largely attributable to the growing size of models, datasets, and computational power.
Simultaneously, a critical pain point arises as several computer vision applications are deploye ...
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...
