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LECTURE 3 LAGRANGE INTERPOLATION

CE30125 - LECTURE 3p. 3 LAGRANGE INTERPOLATION Fit points with an degree polynomial = exact function of which only discrete values are known and used to estab-lish an interpolating or approximating function = approximating or interpolating function. This function will pass through allspecified INTERPOLATION points (also referred to as data points or nodes).N1+Nthf1x0g(x)f(x ) N1+gx gx N1+CE30125 - LECTURE 3p. The INTERPOLATION points or nodes are given as:: There exists only one degree polynomial that passes through a given set of points. It s form is (expressed as a power series):where = unknown coefficients, ( coefficients). No matter how we derive the degree polynomial, Fitting power series LAGRANGE interpolating functions Newton forward or backward interpolationThe resulting polynomial will always be the same!

Power Series Fitting to Define Lagrange Interpolation • must match at the selected data points : : • Solve set of simultaneous equations • It is relatively computationally costly to solve the coefficients of the interpolating func-tion (i.e. you need to program a solution to these equations). gx fx gx o = f o a o a 1 x o a 2 x o 2 a N x o

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