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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 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)

- Stephen D. Shank
- 2014

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 Krylov subspaces to solve equations which may viewed as extensions of the classical Lyapunov and Sylvester equations. The first class of matrix equations that we… (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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