Lecture20101111_1

Lecture20101111_1 - Numerical Analysis II Dr Abigail Wacher...

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Numerical Analysis II Dr Abigail Wacher Nov 11, 2010 1 3. Polynomial Interpolation When presented with n C 1 data points x i , fx = 0, 1,. .., we may want to draw a curve to go through these points in order to obtain some information, that is by interpolation or extrapolation of values of yx which are unknown. Interpolation uses data points to predict values of where s and e 0 , Extrapolation uses data points to predict values of for s , O or ! 0 Definition A polynomial, p , has a degree if = a 0 C 1 C 2 2 C ... C where 0 , 1 ,..., are real numbers and s 0. Call nodes or abscissae. is an interpolating polynomial if px = for = 0, 1,. .., Given C 1 data points, a polynomial fit chooses a polynomial to go though all C 1 data points and where the j = 0, 1,. .., are chosen to satisfy the requirements: = y , = 0, 1,. .., 0 = 0 C K 1 0 K 1 C ... C 1 0 C 0 ... = C K 1 K 1 C ... C 1 C 0 This is a system of C 1 equations with C 1 unknowns. This can be written,

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Lecture20101111_1 - Numerical Analysis II Dr Abigail Wacher...

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