Related papers: On the Block-Decomposability of 1-Parameter Matrix…
The exact/approximate non-orthogonal general joint block diagonalization ({\sc nogjbd}) problem of a given real matrix set $\mathcal{A}=\{A_i\}_{i=1}^m$ is to find a nonsingular matrix $W\in\mathbb{R}^{n\times n}$ (diagonalizer) such that…
For a symmetric positive semidefinite linear system of equations $\mathcal{Q} {\bf x} = {\bf b}$, where ${\bf x} = (x_1,\ldots,x_s)$ is partitioned into $s$ blocks, with $s \geq 2$, we show that each cycle of the classical block symmetric…
Recent advances in MCMC use normalizing flows to precondition target distributions and enable jumps to distant regions. However, there is currently no systematic comparison of different normalizing flow architectures for MCMC. As such, many…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
A strategy to construct physics-based local surrogate models for parametric Stokes flows and coupled Stokes-Darcy systems is presented. The methodology relies on the proper generalized decomposition (PGD) method to reduce the dimensionality…
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…
We present a new class of particle methods with deformable shapes that converge in the uniform norm without requiring remappings, extended overlapping or vanishing moments for the particles. The crux of the method is to use polynomial…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
Increasing production and exchange of multimedia content has increased the need for better protection of copyright by means of watermarking. Different methods have been proposed to satisfy the tradeoff between imperceptibility and…
A Koopman decomposition is a powerful method of analysis for fluid flows leading to an apparently linear description of nonlinear dynamics in which the flow is expressed as a superposition of fixed spatial structures with exponential time…
We develop an abstract theory of flows of geometric $H$-structures, i.e., flows of tensor fields defining $H$-reductions of the frame bundle, for a closed and connected subgroup $H\subset SO(n)$, on any connected and oriented $n$-manifold…
Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more…
Aerodynamic loads play a central role in many fluid dynamics applications, and we present a method for identifying the structures (or modes) in a flow that make dominant contributions to the time-varying aerodynamic loads in a flow. The…
The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…
Flow equation methods, more generally known as Similarity Renormalization Group (SRG) techniques, were developed to address multiscale problems where multiple length or energy scales contribute simultaneously. In this Thesis, we formulate…
Statistical inference for stochastic block models typically relies on the spectrum of the normalized adjacency matrix $\A^*$. In practice, the true probability matrix $\mathbf{B}$ is unknown and must be replaced by a plug-in estimator…
Concurrent separation logics have helped to significantly simplify correctness proofs for concurrent data structures. However, a recurring problem in such proofs is that data structure abstractions that work well in the sequential setting…
This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structure which has a unique linear-sized decomposition tree. We derive an O(n^2) decomposition algorithm and we take…
Some fast algorithms for computing the eigenvalues of a block companion matrix $A = U + XY^H$, where $U\in \mathbb C^{n\times n}$ is unitary block circulant and $X, Y \in\mathbb{C}^{n \times k}$, have recently appeared in the literature.…