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Interpolation - Chapter 19 Interpolation 19.1...

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Chapter 19 Interpolation 19.1 One-Dimensional Interpolation Empirical data obtained experimentally often times conforms to a fixed (deterministic) but unkown functional relationship. When estimates of other points on the function are required, procedures for obtaining those estimates falls under the general category of Interpolation. The simplest case occurs when the data consists of a set of points each made up of an independent variable and a single dependent variable observation. The MATLAB function ' interp1 ' default mode is designed to linearly interpolate, as in a Table Lookup, empirical data to estimate the unknown function corresponding to a set of independent variable values. For example, suppose a consumer testing magazine is interested in the repair costs for a particular luxury passenger vehicle after its been in an accident. The test procedure calls for head-on collisions of the vehicle with a stationary object at various speeds. The cost of restoring the vehicle to its pre- crash condition is determined. Tabulated results after several collisions are given below. Speed ( S ) mph Damages ( D ) $ 5 4500 10 12150 20 23750 30 43500 40 61000 The first example demonstrates how to estimate the unknown function D = f ( S ), which generated the tabulated data points, at other speeds between 5 and 40 mph.
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