Stephen D. Shank

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We consider the numerical approximation to the solution of the matrix equation A 1 X + XA 2 − Y C = 0 in the unknown matrices X, Y , under the constraint XB = 0, with A 1 , A 2 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)
SUMMARY 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(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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