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 matrix with ones and zeros, which satisfies the Pólya condition, may be regular and singular for Birkhoff interpolation. We prove that for random distributed ones, is singular with probability that converges to one if , . Previously, this was known only if . For constant and , the probability is asymptotically at least .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1981-0632539-0

Keywords:
Birkhoff interpolation,
Pólya matrix,
regularity and singularity,
coalescence of rows,
probability of singularity,
hypergeometric distribution

Article copyright:
© Copyright 1981
American Mathematical Society