Computing the Homology of Real Projective Sets

We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algorithm is numerically stable (in a sense to be made precise). Its cost depends on the condition of the input as well as on...

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Detalles Bibliográficos
Autores principales: Cucker, F., Krick, T., Shub, M.
Formato: JOUR
Materias:
Complexity
Condition
Exponential time
Homology groups
Real projective varieties
Computational methods
Mathematical techniques
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_16153375_v18_n4_p929_Cucker
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algorithm is numerically stable (in a sense to be made precise). Its cost depends on the condition of the input as well as on its size and is singly exponential in the number of variables (the dimension of the ambient space) and polynomial in the condition and the degrees of the defining polynomials. In addition, we show that outside of an exceptional set of measure exponentially small in the size of the data, the algorithm takes exponential time. © 2017, SFoCM.

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