Spline Interpolation Method Electrical Engineering Majors Authors Autar
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Spline Interpolation Method Electrical Engineering Majors Authors: Autar Kaw, Jai Paul http: //numericalmethods. eng. usf. edu Transforming Numerical Methods Education for STEM Undergraduates http: //numericalmethods. eng. usf. edu 1
Spline Method of Interpolation http: //numericalmethods. eng. usf. edu
What is Interpolation ? Given (x 0, y 0), (x 1, y 1), …… (xn, yn), find the value of ‘y’ at a value of ‘x’ that is not given. 3 lmethods. eng. usf. edu http: //numerica
Interpolants Polynomials are the most common choice of interpolants because they are easy to: Evaluate Differentiate, and Integrate. 4 lmethods. eng. usf. edu http: //numerica
Why Splines ? 5 lmethods. eng. usf. edu http: //numerica
Why Splines ? 6 Figure : Higher order polynomial interpolation is a bad ideahttp: //numerica lmethods. eng. usf. edu
Linear Interpolation 7 lmethods. eng. usf. edu http: //numerica
Linear Interpolation (contd) 8 lmethods. eng. usf. edu http: //numerica
Example Thermistors are based on materials’ change in resistance with temperature. A manufacturer of thermistors makes the following observations on a thermistor. Determine the temperature corresponding to 754. 8 ohms using linear spline interpolation. 9 R (Ω) T(°C) 1101. 0 911. 3 636. 0 451. 1 25. 113 30. 131 40. 120 50. 128 lmethods. eng. usf. edu http: //numerica
Linear Interpolation 10 lmethods. eng. usf. edu http: //numerica
Quadratic Interpolation 11 lmethods. eng. usf. edu http: //numerica
Quadratic Interpolation (contd) 12 lmethods. eng. usf. edu http: //numerica
Quadratic Splines (contd) 13 lmethods. eng. usf. edu http: //numerica
Quadratic Splines (contd) 14 lmethods. eng. usf. edu http: //numerica
Quadratic Splines (contd) 15 lmethods. eng. usf. edu http: //numerica
Example Thermistors are based on materials’ change in resistance with temperature. A manufacturer of thermistors makes the following observations on a thermistor. Determine the temperature corresponding to 754. 8 ohms using quadratic spline interpolation. 16 R (Ω) T(°C) 1101. 0 911. 3 636. 0 451. 1 25. 113 30. 131 40. 120 50. 128 lmethods. eng. usf. edu http: //numerica
Solution 17 lmethods. eng. usf. edu http: //numerica
Solution (contd) 18 lmethods. eng. usf. edu http: //numerica
Solution (contd) 19 lmethods. eng. usf. edu http: //numerica
Solution (contd) 20 lmethods. eng. usf. edu http: //numerica
Solution (contd) 21 lmethods. eng. usf. edu http: //numerica
Solution (contd) 22 lmethods. eng. usf. edu http: //numerica
Additional Resources For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, Math. Cad and MAPLE, blogs, related physical problems, please visit http: //numericalmethods. eng. usf. edu/topics/spline_met hod. html
THE END http: //numericalmethods. eng. usf. edu
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