Lecture20101118_1

Lecture20101118_1 - Numerical Analysis II Dr Abigail Wacher...

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Numerical Analysis II Dr Abigail Wacher Nov 18, 2010 1 Two drawbacks of Lagrange formula for obtaining the interpolating polynomial. 1) To evaluate the polynomial there is a lot of arithmetic. 2) If a new node is added to the date say x n C 1 and we wish to include it in the interpolation, then we would need to construct a new set of Langrange coefficients. We now consider a different Formula to obtain the unique polynomial. The Newton Formula In the Lagrange formula the polynomials L 0 , 1 ,..., are chosen as the basis for the linear space of polynomials of degree at most , and p is taken to be a linear combination of these basis elements. The Newton polynomials w 0 , i ,..., defined as 0 d 1 d K 0 K 1 ... K K 1 = ? j = 0 K 1 K = 1, 2,. .., form a basis for the polynomials of degree at most . The Newton Formula is: = fx 0 0 C 0 , 1 1 C ... C 0 , 1 ,..., where the Newton polynomials are meant to interpolate the given data at nodes 0 , 1 ,..., We need to find 0 ,..., 0 = 0 = 0 1 = 1 = 0 C 0 , 1 1 K 0 2 = 2 = 0 C 0 , 1 2 K
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This note was uploaded on 02/09/2011 for the course MATH 2051 taught by Professor Dr.a.wacher during the Fall '11 term at Durham.

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Lecture20101118_1 - Numerical Analysis II Dr Abigail Wacher...

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