Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1981-0632539-0
MathSciNet review: 632539
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $\tfrac {1} {2}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 41A05, 05B20, 15A52, 60C05

Retrieve articles in all journals with MSC: 41A05, 05B20, 15A52, 60C05


Additional Information

Keywords: Birkhoff interpolation, Pólya matrix, regularity and singularity, coalescence of rows, probability of singularity, hypergeometric distribution
Article copyright: © Copyright 1981 American Mathematical Society