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Computing the homology of basic semialgebraic sets

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If you have a question about this talk, please contact Hamza Fawzi.

We describe a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of a basic semialgebraic set. The algorithm is numerically stable in the sense that the precision required to guarantee a correct output depends on the condition number of the data and it is polynomially small. Its running time also depends on this condition but it is bounded by a singly exponential bound on the size of the input out of a vanishingly small set of data. All algorithms previously proposed for this problem have a complexity which is doubly exponential (and this is so for almost all data).

This is joint work with Felipe Cucker and Pierre Lairez.

This talk is part of the Applied and Computational Analysis series.

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