Solution-Recovery in L1-norm for Non-square Linear Systems: Deterministic Conditions and Open Questions
Consider an over-determined linear system A'x = b and an under-determined linear system By = c. Given b = A'x* + h, under what conditions x* will minimize the residual A'x - b in L1-norm? On the other hand, given c = Bh, under what conditions h will be the minimum L1-norm solutio to By = c? These two ``solution-recovery'' problems have been the focus of a number of recent works. Moreover, these two problems are equivalent under appropriate conditions on the data sets (A,b) and (B,c). In this paper, we give deterministic conditions for these solution-recoverary problems and raise a few open questuions. Some of the results in this paper are already known or partially known, but our derivations are different and thus may provide different perspectives.
Citable link to this pagehttps://hdl.handle.net/1911/102038
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