53 citations · 137 across the 21 of their papers we have counts for
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math.DS2015★ 8 cited
Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
R. Castelli, M. Gameiro, J. -P. Lessard
In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is appl…
math.NA2015★ 25 cited
Continuation of Point Clouds via Persistence Diagrams
Marcio Gameiro, Yasuaki Hiraoka, Ippei Obayashi
In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persi…