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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Probability and interpolation
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by G. G. Lorentz and R. A. Lorentz PDF
Trans. Amer. Math. Soc. 268 (1981), 477-486 Request permission

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
  • © Copyright 1981 American Mathematical Society
  • 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