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we present a brief matlab tutorial cov-ering only the bare-minimum that a beginner 7 apr 201011 apr 2011 interpolates with a hermite cubic polynomial using the function values and piecewise hermite cubic interpolation between 2 points knowing s = spline( x , y , xq ) returns a vector of interpolated values s corresponding to the query points in …
The first theorem is that the Hermite polynomials can be obtained from a generating function. The derivation of generating functions is something of a black art, and as it requires the use of complex variable theory (in particular, Cauchy’s integral formula) but we’ll just accept it without proof for now. The result is e åz2+2zx = ¥ n=0 zn n! H n(x) (1) Here z is a dummy variable which
pchip interpolates using a piecewise cubic polynomial P ( x) with these properties: On each subinterval x k ≤ x ≤ x k + 1 , the polynomial P ( x) is a cubic Hermite interpolating polynomial for the given data points with specified derivatives (slopes) at the interpolation points. P ( x) interpolates y , that is, P ( x j) = y j, and the The representation of the Hermite polynomial in terms of Lagrange polynomials and their derivatives is not practical, because of the di culty of di erentiating and evaluating these polyno-mials. Instead, one can construct the Hermite polynomial using a Newton divided-di erence table, in which each entry corresponding to two identical interpolation points is lled with the value of f0(x) at the

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