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Unformatted text preview: 05.05.1 Chapter 05.05 Spline Method of Interpolation – More Examples Electrical Engineering Example 1 Thermistors are used to measure the temperature of bodies. Thermistors are based on materials’ change in resistance with temperature. To measure temperature, manufacturers provide you with a temperature vs. resistance calibration curve. If you measure resistance, you can find the temperature. A manufacturer of thermistors makes several observations with a thermistor, which are given in Table 1. Table 1 Temperature as a function of resistance. R ohm T C 1101.0 911.3 636.0 451.1 25.113 30.131 40.120 50.128 05.05.2 Chapter 05.05 Figure 1 Resistance vs. temperature. Determine the temperature corresponding to 754.8 ohms using linear splines. Solution Since we want to find the temperature at 8 . 754 R and we are using linear splines, we need to choose the two data points that are closest to 8 . 754 R that also bracket 8 . 754 R to evaluate it. The two points are 3 . 911 R and . 636 1 R . Then , 3 . 911 R 131 . 30 ) ( R T , . 636 1 R 120 . 40 ) ( 1 R T given ) ( ) ( ) ( ) ( ) ( 1 1 R R R R R T R T R T R T 3 . 911 . 636 ), 3 . 911 ( 3 . 911 . 636 131 . 30 120 . 40 131 . 30 R R Hence ) 3 . 911 ( 036284 . 131 . 30 ) ( R R T At , 8 . 754 R ) 3 . 911 8 . 754 ( 036284 . 131 . 30 ) 8 . 754 ( T C 809 . 35 Linear spline interpolation is no different from linear polynomial interpolation. Linear splines still use data only from the two consecutive data points. Also at the interior points of the data, Spline Method of InterpolationMore Examples: Electrical Engineering 05.05.3 the slope changes abruptly. This means that the first derivative is not continuous at these points. So how do we improve on this? We can do so by using quadratic splines. Example 2 Thermistors are used to measure the temperature of bodies. Thermistors are based on materials’ change in resistance with temperature. To measure temperature, manufacturers provide you with a temperature vs. resistance calibration curve. If you measure resistance, provide you with a temperature vs....
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 Spring '08
 Kaw,A

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