Dictionary:Lagrange interpolation formula

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{{#category_index:L|Lagrange interpolation formula}} (l∂ granj’) A method of calculating a polynomial for interpolating between a set of values which are not necessarily equally spaced.

y1=y(x1),y2=y(x2),...,yn=y(xn);


y(x)=[(xx2)(xx3)...(xxn)/(x1x2)...(x1xn)]y1+[(xx1)(xx3)...(xxn)/(x2x1)...(x2xn)]y2+...+[(xx1)(xx2)...(xxn–1)/(xnx2)...(xnxn–1)]yn,


that is, in the factors multiplying yk the factor (xxk) is omitted. Named for Joseph Louis Lagrange (1736–1813), French mathematician.