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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 ...
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 ...
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 the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...
Interface stress is a fundamental descriptor for interphase boundaries and is defined in strict relation to the interface energy. In nanomultilayers with their intrinsically high interface density, the functional properties are dictated by the interface st ...
For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the generaliz ...
In this paper we demonstrate ultra-high sensitivity silicon nanowires pH and protein sensing on the same Silicon nanowire array platform by using a constant current method and monitoring the drain voltage as function of analyte concentration. The injected ...
Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projecti ...
Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...
In this paper, we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in [B. Kirchheim, S. Muller and V. S(sic)ver & aacute;k, Studying Nonlinear PDE by ...
