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

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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 $\tfrac {1} {2}$.

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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