## Lebesgue Constants (Lagrange Interpolation)

N.B. A detailed on-line essay by S. Finch was the starting point for this entry.

Define the th Lebesgue constant for the Lagrange Interpolating Polynomial by

 (1)

It is true that
 (2)

The efficiency of a Lagrange interpolation is related to the rate at which increases. Erdös (1961) proved that there exists a Positive constant such that
 (3)

for all . Erdös (1961) further showed that
 (4)

so (3) cannot be improved upon.

References

Erdös, P. Problems and Results on the Theory of Interpolation, II.'' Acta Math. Acad. Sci. Hungary 12, 235-244, 1961.

Finch, S. Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/lbsg/lbsg.html

© 1996-9 Eric W. Weisstein
1999-05-26