Geodesic
Probabilistic and numerical validation of homology computations for nodal domains
Day, Sarah1 ; Kalies, William2 ; Mischaikow, Konstantin3 ; Wanner, Thomas4
1 College of William and Mary, Department of Mathematics, P.O. Box 8795, Williamsburg, VA 23187
2 Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431
3 Department of Mathematics, Rutgers University, 110 Frelinghusen Road, Piscataway, NJ 08854
4 Department of Mathematical Sciences, George Mason University, 4400 University Drive, MS 3F2, Fairfax, VA 22030
Electronic research announcements of the American Mathematical Society, Tome 13 (2007), pp. 60-73.

Voir la notice de l'article provenant de la source American Mathematical Society

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 Fourier series in one and two space dimensions, which furnishes explicit probabilistic a-priori bounds for the suitability of certain discretization sizes. In addition, we introduce a numerical method for verifying the homology computation using interval arithmetic.
DOI : 10.1090/S1079-6762-07-00175-8

Day, Sarah 1 ; Kalies, William 2 ; Mischaikow, Konstantin 3 ; Wanner, Thomas 4

1 College of William and Mary, Department of Mathematics, P.O. Box 8795, Williamsburg, VA 23187
2 Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431
3 Department of Mathematics, Rutgers University, 110 Frelinghusen Road, Piscataway, NJ 08854
4 Department of Mathematical Sciences, George Mason University, 4400 University Drive, MS 3F2, Fairfax, VA 22030 
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Day, Sarah; Kalies, William; Mischaikow, Konstantin; Wanner, Thomas. Probabilistic and numerical validation of homology computations for nodal domains. Electronic research announcements of the American Mathematical Society, Tome 13 (2007), pp. 60-73. doi : 10.1090/S1079-6762-07-00175-8. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-07-00175-8/

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