“Hermite's Interpolating Polynomial”的概念、定义、习题解题方法及翻译-数学辞典

单词

Hermite's Interpolating Polynomial

释义

Hermite's Interpolating Polynomial

Let be an th degree Polynomial with zeros at , ..., . Then the fundamentalPolynomials are

(1)

and

(2)

for

, 2, ...

. These polynomials have the properties

for

, 2, ...,

. Now let

, ...,

and

, ...,

be values. Then the expansion

(7)

gives the unique Hermite interpolating fundamental polynomial for which

			(8)
			(9)

, these are called Step Polynomials. The fundamental polynomials satisfy

(10)

and

(11)

Also, if

is an arbitrary distribution on the interval

, then

where

are Christoffel Numbers.
References

Hildebrand, F. B. Introduction to Numerical Analysis. New York: McGraw-Hill, pp. 314-319, 1956.

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., pp. 330-332, 1975.

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