For a given set of data points t,..., tn, define the function (t) by T(t) =...
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For a given set of data points t₁,..., tn, define the function π(t) by T(t) = (t-t₁)(t-t₂)... (t - tn) Show that T' (t) = (tj-t₁)... (tj — tj-1)(tj — tj+¹1)... (tj - tn) (b) [15%] Use the result of part (a) to show that the jth Lagrange basis function can be expressed as lj (t) = = π (t) (t-tj)π' (tj) For a given set of data points t₁,..., tn, define the function π(t) by T(t) = (t-t₁)(t-t₂)... (t - tn) Show that T' (t) = (tj-t₁)... (tj — tj-1)(tj — tj+¹1)... (tj - tn) (b) [15%] Use the result of part (a) to show that the jth Lagrange basis function can be expressed as lj (t) = = π (t) (t-tj)π' (tj)
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