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Probabilistic validation of homology com...
Mischaikow, Konstant...

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Probabilistic validation of homology computations for nodal domains by Mischaikow, Konstantin ( Author )
Lemonjar Open Access
N.A
31-07-2007
Homology has long been accepted as an important computable tool for quantifying complex structures. In many applications, these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study based on suitable discretizations. Such an approach immediately raises the question of how accurate the resulting homology computations are. In this paper, we present a probabilistic approach to quantifying the validity of homology computations for nodal domains of random fields in one and two space dimensions, which furnishes explicit probabilistic a priori bounds for the suitability of certain discretization sizes. We illustrate our results for the special cases of random periodic fields and random trigonometric polynomials.
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English
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MYR 0.00
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https://arxiv.org/abs/0707.4588
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