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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Probability and interpolation


Authors: G. G. Lorentz and R. A. Lorentz
Journal: Trans. Amer. Math. Soc. 268 (1981), 477-486
MSC: Primary 41A05; Secondary 05B20, 15A52, 60C05
MathSciNet review: 632539
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Abstract: An $ m \times n$ matrix $ E$ with $ n$ ones and $ (m - 1)n$ zeros, which satisfies the Pólya condition, may be regular and singular for Birkhoff interpolation. We prove that for random distributed ones, $ E$ is singular with probability that converges to one if $ m$, $ n \to \infty $. Previously, this was known only if $ m \geqslant (1 + \delta )n/\log n$. For constant $ m$ and $ n \to \infty $, the probability is asymptotically at least $ \tfrac{1} {2}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0632539-0
PII: S 0002-9947(1981)0632539-0
Keywords: Birkhoff interpolation, Pólya matrix, regularity and singularity, coalescence of rows, probability of singularity, hypergeometric distribution
Article copyright: © Copyright 1981 American Mathematical Society