CSC_349_HANDOUT#19

CSC_349_HANDOUT#19 - z lies outside of the interval...

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1 COMPUTER SCIENCE 349A Handout Number 19 Section 18.2 POLYNOMIAL INTERPOLATION Let ) ( x f y = be any given function. For any value of n 0 and any given values n x x x , , , 1 0 K , let ) ( i i x f y = . The polynomial interpolation problem is to determine a polynomial ) ( x P of degree less than or equal to n for which . , , 1 , 0 for ) ( n i y x P i i K = = The set of n + 1 data points ( x i , y i ) may be the only functional values known (that is, ) ( x f is a discrete function , which could occur for example with experimental data) or ) ( x f may be a known continuous function and the n + 1 data points ( x i , y i ) are a finite sample of values with ) ( i i x f y = . If z is some value between 2 of the given values x i and if ) ( z P is computed as an approximation to ) ( z f , then this approximation to ) ( z f is said to be determined by polynomial interpolation . On the other hand, if
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Unformatted text preview: z lies outside of the interval containing all of the values x i and if ) ( z P is computed as an approximation to ) ( z f , then this approximation to ) ( z f is said to be determined by polynomial extrapolation . Note that an interpolating polynomial and the Taylor polynomial both determine polynomial approximations to ) ( x f . However, in general they are very different approximations to ) ( x f . Note that an interpolating polynomial uses the information ) ( , ), ( ), ( 1 1 n n x f y x f y x f y = = = K to determine the polynomial approximation, whereas the Taylor polynomial uses the information ) ( , ), ( ), ( ) ( x f x f x f n K ′ to determine the polynomial approximation....
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This note was uploaded on 12/10/2011 for the course CSC 349 taught by Professor Oadje during the Spring '11 term at University of Victoria.

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