N9 - ME 510 NUMERICAL METHODS FOR ME II INTERPOLATION...

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ME 510 NUMERICAL METHODS FOR ME II Prof. Dr. Faruk Arınç Fall 2010 INTERPOLATION SCHEMES Name Advantages Disadvantages Newton-Gregory The order of the polynomial can be changed easily. Evaluation of errors is easy. A difference or a divided difference table must be prepared. Lagrange Convenient form. Easy to program. Cumbersome for hand calculations. Spline Applicable to any number of data points. Needs to solve a set of simultaneous equations. Hermite Accuracy is high because polynomial is fitted to derivatives also. Needs values of derivatives. Chebyshev Errors are more evenly distributed than that with an equispaced grid. Unevenly distributed grid points. ME 510 NUMERICAL METHODS FOR ME II Prof. Dr. Faruk Arınç Fall 2010 Define Newton-Gregory Forward Polynomial 0 x - x s where h is constant (equally spaced data points) h g32 f ! n 1) n - (s ... 1) - (s s ... f ! 2 1) - (s s f s f (x) P 0 n 0 2 0 0 n g39 g14 g14 g14 g39 g14 g39 g14 g32 ) ( f )! 1 (n ) x - (x ... ) x - (x ) x - (x (x) E ) ( f h )! 1 (n n) - (s ... 2) - (s 1) - (s s (x) E 1) (n n 1 0 1) (n 1 n g91 g91 g14 g14 g14 g14 g32 g14 g32 Error: To estimate the error, replace the (n+1)th derivative with (n+1)th divided difference.
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