Stephen D. Shank

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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)
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)
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)
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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