## 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 $\tfrac {1} {2}$.## References

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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