Austin R. Benson

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—The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called " tall-and-skinny matrices, " there is a numerically stable, efficient, communication-avoiding algorithm for computing the QR factoriza-tion. It has been(More)
Numerous algorithms are used for nonnegative matrix fac-torization under the assumption that the matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than columns, so-called " tall-and-skinny matrices ". One key component to these improved methods is an orthogonal matrix(More)
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substruc-tures such as triangles, cycles, and feed-forward loops. Here we(More)
Errors due to hardware or low level software problems, if detected, can be fixed by various schemes, such as recomputation from a checkpoint. Silent errors are errors in application state that have escaped low-level error detection. At extreme scale, where machines can perform astronomically many operations per second, silent errors threaten the validity of(More)
Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic process. A standard way to compute this distribution for a random walk on a finite set of states is to compute the(More)
Fast algorithms for matrix multiplication, or those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Aside from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications. However, there exist many practical(More)
Using random graphs to model networks has a rich history. In this paper, we analyze and improve the multifractal network generators (MFNG) introduced by Palla <i>et al</i>. We provide a new result on the probability of subgraphs existing in graphs generated with MFNG. This allows us to quickly compute moments of an important set of graph properties, such as(More)