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- Stephen D. Shank, Valeria Simoncini, Daniel B. Szyld
- Numerische Mathematik
- 2016

- Stephen D. Shank, Valeria Simoncini
- SIAM J. Matrix Analysis Applications
- 2013

We consider the numerical approximation to the solution of the matrix equation A1X+XA2 −Y C = 0 in the unknown matrices X, Y , under the constraint XB = 0, with A1, A2 of large dimensions. We propose a new formulation of the problem that entails the numerical solution of an unconstrained Sylvester equation. The spectral properties of the resulting… (More)

This note is a first attempt to perform waveform inversion by utilizing recent developments in semidefinite relaxations for polynomial equations to mitigate non-convexity. The approach consists in reformulating the inverse problem as a set of constraints on a low-rank moment matrix in a higher-dimensional space. While this idea has mostly been a theoretical… (More)

- Stephen D. Shank
- 2014

LOW-RANK SOLUTION METHODS FOR LARGE-SCALE LINEAR MATRIX EQUATIONS Stephen D. Shank DOCTOR OF PHILOSOPHY Temple University, May, 2014 Professor Daniel B. Szyld, Chair We consider low-rank solution methods for certain classes of large-scale linear matrix equations. Our aim is to adapt existing low-rank solution methods based on standard, extended and rational… (More)

- Russell A Hermansen, Benjamin P Oswald, +5 authors David A Liberles
- Journal of Molecular Evolution
- 2017

With the large collections of gene and genome sequences, there is a need to generate curated comparative genomic databases that enable interpretation of results in an evolutionary context. Such resources can facilitate an understanding of the co-evolution of genes in the context of a genome mapped onto a phylogeny, of a protein structure, and of… (More)

- David Fritzsche, Andreas Frommer, Stephen D. Shank, Daniel B. Szyld
- SIAM J. Scientific Computing
- 2013

Starting from a partitioning of an edge-weighted graph into subgraphs, we develop a method which enlarges the respective sets of vertices to produce a decomposition with overlapping subgraphs. The vertices to be added when growing a subset are chosen according to a criterion which measures the strength of connectivity with this subset. By using our method… (More)

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