Numerical Methods for Unequal Intervals

Autor: I.M. Khabaza
Rok vydání: 1965
Předmět:
DOI: 10.1016/b978-0-08-010774-5.50013-7
Popis: This chapter describes the numerical methods for unequal intervals. Given the values y 0 , y 1 , y 2 , …, y n of a function f ( x ) at the n + 1 distinct points x = x 0 , x 1 , x 2 , …, x n , one wish to estimate y at some other value x . One approximate f ( x ) by a polynomial and, in particular, choosing one which passes through the points ( x 0 , y 0 ), ( x 1 y 1 ),…, ( x n , y n ). There is a unique polynomial of degree n through these n + 1 points. It is found that for if there were two such polynomials, h ( x ) and g ( x ) then h ( x ) − g ( x ) would be a polynomial of degree n at most with n + 1 zeros at x = x 0 , x 1 ,. .., x n . This is impossible, so h ( x ) − g ( x ) must be identically zero hence h ( x ) is unique.
Databáze: OpenAIRE
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