Transcription of Chapter 3 Interpolation - MathWorks
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Chapter 3 Interpolation - MathWorks
Chapter 3 InterpolationInterpolation is the process of defining a function that takes on specified values atspecified points. This Chapter concentrates on two closely related interpolants: thepiecewise cubic spline and the shape-preserving piecewise cubic named pchip. The Interpolating PolynomialWe all know that two points determine a straight line. More precisely, any twopoints in the plane, (x1,y1) and (x2,y2), withx1 =x2, determine a unique first-degree polynomial inxwhose graph passes through the two points. There aremany different formulas for the polynomial, but they all lead to the same straightline generalizes to more than two points.
2 Chapter 3. Interpolation There are n terms in the sum and n − 1 terms in each product, so this expression defines a polynomial of degree at most n−1.If P(x) is evaluated at x = xk, all the products except the kth are zero.Furthermore, the kth product is equal to one, so the sum is equal to yk and the interpolation conditions are satisfied. For example, consider the following data set.
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