We may estimate the position and the speed of the car when the time is t 10 using hermite interpolation. If all we know is function values, this is a reasonable approach. Polynomial interpolators for highquality resampling of. Math 450 the lagrange interpolating polynomial, p x. Hermite interpolation theorem let s be a discrete data set of distinct points defined as follows. Then, the hermite polynomial can be represented using the newton divideddi erence formula.
School of mechanical and manufacturing engineering, national university of science and technology. Drop sample and linear interpolation as such are not adequate for highquality resampling, but even linear interpolation is a big improvement compared to drop sample. The most common interpolation technique is linear interpolation. Piecewise linear interpolation is simply connecting data points by straight lines.
Di erentiation we now discuss how polynomial interpolation can be applied to help solve a fundamental problem from calculus that frequently arises in scienti c applications, the problem of computing the derivative of a given function fx. Interpolation is used to estimate data points between two known points. Note that lagrange interpolation is a special case of hermite interpolation, i. P n, where p n is the set of polynomials of degree at most n. Time 0 3 5 8 distance 0 225 383 623 993 speed 75 77 80 74 72. The following result about existence and uniqueness of p nx has some different proofs, see for example 24,11. Lockheed missiles and space company has installed a largescale automatic data acquisition ada system which ties together the companys manufacturing facilities located in. Both of them fall into the category of piecewise polynomial. Bindel, spring 2012 intro to scienti c computing cs 3220 week 10.