Assume that the polynomial P5(x) interpolates a function f (x) at the six data points ( , f ( ))… 1 answer below »

Assume that the polynomial P5(x) interpolates a function f (x) at the six data points (, f ()) with x-coordinates x1 = 0, x2 = .2, x3 = .4, x4 = .6, x5 = .8, and x6 = 1. Assume that the interpolation error at x = .3 is |f (.3) − P5(.3)| = .01. Estimate the new interpolation error

|f (.3) − P7(.3)| that would result if two additional interpolation points (x6, y6) = (.1, f (.1)) and (x7, y7) = (.5, f (.5)) are added. What assumptions have you made to produce this estimate?

 

 

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