6. Consider f(x)-sinx and evenly spaced nodes 0-0 < xīく… < Zn-2T. Let P(z) be the piecewise cubic interpolant given values and first derivatives of f at the nodes. (a) In the case n = 100, use...
6. Consider f(x)-sinx and evenly spaced nodes 0-0 < xīく… < Zn-2T. Let P(z) be the piecewise cubic interpolant given values and first derivatives of f at the nodes. (a) In the case n = 100, use calculus and the error formula 4! where 1 E [xi,Ti+1], to bound the absolute error lf(1)-P(1) (b) For arbitrary x E [0.2 , use error bounds to determine n ensuring that If(x)- P(x) s 10-10
6. Consider f(x)-sinx and evenly spaced nodes 0-0