Figure 1.1 Linear interpolation assumes that a straight line joins two points f(a) and f(c), and that the value of f(b), where b lies between a and c, lies on this line. Figure 1.2 Cubic spline interpolation is when the points f(a) and f(c) are joined by a cubic polynomial, and the value of f(b), a function of b, which lies between points a and c, lies on this curve. Formula Assumes a<b<c f(b)=f(a)+((b-a)/(c-a))[f(c)-f(a)] Example 1 The data was given, shown in Figure 1.1 at right. Figure 2.1 Example 2 In the example on the left, we used linear interpolation to find the freezing temperature of certain salinities of water. 1. Problem Statement Use linear interpolation to determine the freezing temperature of water with a certain salinity. 2. Input/Output Description Inputs: first salinity, second salinity, first freezing temperature, second freezing temperature, new salinity. Output: new freezing temperature 3. Hand Example See...
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