Newtons Divided Difference Polynomial Method of Interpolation Electrical

Newton’s Divided Difference Polynomial Method of Interpolation 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

Newton’s Divided Difference 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

Newton’s Divided Difference Method Linear interpolation: Given linear interpolant through the data pass a where 5 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 the Newton Divided Difference method for linear interpolation. 6 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 7 lmethods. eng. usf. edu http: //numerica

Linear Interpolation (contd) 8 lmethods. eng. usf. edu http: //numerica

Quadratic Interpolation 9 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 the Newton Divided Difference method for quadratic interpolation. 10 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

Quadratic Interpolation (contd) 11 lmethods. eng. usf. edu http: //numerica

Quadratic Interpolation (contd) 12 lmethods. eng. usf. edu http: //numerica

Quadratic Interpolation (contd) 13 lmethods. eng. usf. edu http: //numerica

General Form where Rewriting 14 lmethods. eng. usf. edu http: //numerica

General Form 15 lmethods. eng. usf. edu http: //numerica

General form 16 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 the Newton Divided Difference method for cubic interpolation. 17 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

Example 18 lmethods. eng. usf. edu http: //numerica

Example 19 lmethods. eng. usf. edu http: //numerica

Example 20 lmethods. eng. usf. edu http: //numerica

Comparison Table 21 lmethods. eng. usf. edu http: //numerica

Actual Calibration R (Ω) 1101. 0 911. 3 636. 0 451. 1 22 T (°C) 25. 113 30. 131 40. 120 50. 128 x(ln R) 7. 0040 6. 8149 6. 4552 6. 1117 y(1/T) 0. 039820 0. 033188 0. 024925 0. 019949 lmethods. eng. usf. edu http: //numerica

Actual Calibration 23 lmethods. eng. usf. edu http: //numerica

Actual Calibration 24 lmethods. eng. usf. edu http: //numerica

Actual Calibration 25 lmethods. eng. usf. edu http: //numerica

Actual Calibration 26 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/newton_div ided_difference_method. html

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