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Full-Text Articles in Mathematics
Uniform Uncertainty Principle And Signal Recovery Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin
Uniform Uncertainty Principle And Signal Recovery Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin
CMC Faculty Publications and Research
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-minimization. Our algorithm, ROMP, reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the uniform uncertainty principle.
Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen
Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen
All HMC Faculty Publications and Research
We consider traveling wave phenomena for a viscoelastic generalization of Burgers' equation. For asymptotically constant velocity profiles we find three classes of solutions corresponding to smooth traveling waves, piecewise smooth waves, and piecewise constant (shock) solutions. Each solution type is possible for a given pair of asymptotic limits, and we characterize the dynamics in terms of the relaxation time and viscosity.