Mathematics, 04.04.2020 04:41 piggygirl211
The function f ( x ) = cos( Οx ) for x β [0 , 1] is approximated by the following piecewise polynomial p of degree β€ 3. The interval [0 , 1] is divided into k subintervals [ a j β 1 ,a j ] with a j = j/k for j = 0 , 1 ,...,k , and in each subinterval p is the polynomial interpolating f at 4 equally spaced points: a j β 1 , a j β 1 + 1 / (3 k ), a j β 1 + 2 / (3 k ), and a j . How should k be chosen so that the error max 0 β€ x β€ 1 | f ( x ) β p ( x ) |β€ 10 β 8 ? That is, derive an error upper bound, find the magnitude of | f (4) ( x ) | , and next get the desired value of k .
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The function f ( x ) = cos( Οx ) for x β [0 , 1] is approximated by the following piecewise polynomi...
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