Related papers: An Abstraction-Preserving Block Matrix Implementat…
Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing recovery algorithms (Bajwa and Mixon, 2012). In this paper, we characterize two block coherence metrics: worst-case and average…
Hierarchical matrix computations have attracted significant attention in the science and engineering community as exploiting data-sparse structures can significantly reduce the computational complexity of many important kernels. One…
Existing approaches to distributed matrix computations involve allocating coded combinations of submatrices to worker nodes, to build resilience to stragglers and/or enhance privacy. In this study, we consider the challenge of preserving…
Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…
The discretization of non-local operators, e.g., solution operators of partial differential equations or integral operators, leads to large densely populated matrices. $\mathcal{H}^2$-matrices take advantage of local low-rank structures in…
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…
The matrix product representation provides a useful formalism to study not only entangled states, but also entangled operators in one dimension. In this paper, we focus on unitary transformations and show that matrix product operators that…
We describe a Maple package that serves at least four purposes. First, one can use it to compute whether or not a given polyhedral structure is Zometool constructible. Second, one can use it to manipulate Zometool objects, for example to…
Traditional optimizing compilers rely on rewrite rules to iteratively apply program transformations. This iterative approach hides optimization opportunities behind intermediate transformation steps. For instance, vectorization can only be…
We develop a calculus that gives an elementary approach to enumerate partition-like objects using an infinite upper-triangular number-theoretic matrix. We call this matrix the Partition-Frequency Enumeration (PFE) matrix. This matrix…
We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our description is local, which offers the potential to speed up…
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the…
Hierarchical optimization architectures are used in power systems to manage disturbances and phenomena that arise at multiple spatial and temporal scales. We present a graph modeling abstraction for representing such architectures and an…
The parallel algorithm for loading large sparse matrices from files into distributed memories of high performance computing (HPC) systems is presented. This algorithm was designed specially for matrices stored in files in the space-effcient…
A program execution monitor is a program that collects and abstracts information about program executions. The "collect" operator is a high level, general purpose primitive which lets users implement their own monitors. "Collect" is built…
Mathematical morphology (MM) is a powerful and widely used framework in image processing. Through set-theoretic and discrete geometric principles, MM operations such as erosion, dilation, opening, and closing effectively manipulate digital…
The multiplication of a sparse matrix with a dense vector (SpMV) is a key component in many numerical schemes and its performance is known to be severely limited by main memory access. Several numerical schemes require the multiplication of…
A task-based formulation of Scalable Universal Matrix Multiplication Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is applied to the multiplication of hierarchy-free, rank-structured matrices that appear in the…
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topological data analysis where matrix reduction is the major…
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…