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Newton’s Divided Difference Polynomial Method of Interpolation. Computer Engineering Majors Authors: Autar Kaw, Jai Paul http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates.

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Newton s divided difference polynomial method of interpolation

Newton’s Divided Difference Polynomial Method of Interpolation

Computer Engineering Majors

Authors: Autar Kaw, Jai Paul

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for STEM Undergraduates

http://numericalmethods.eng.usf.edu


Newton s divided difference method of interpolation http numericalmethods eng usf edu
Newton’s Divided Difference Method of Interpolation Interpolationhttp://numericalmethods.eng.usf.edu


What is interpolation
What is Interpolation ? Interpolation

Given (x0,y0), (x1,y1), …… (xn,yn), find the value of ‘y’ at a value of ‘x’ that is not given.

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Interpolants
Interpolants Interpolation

Polynomials are the most common choice of interpolants because they are easy to:

  • Evaluate

  • Differentiate, and

  • Integrate.

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Newton s divided difference method
Newton’s Divided Difference Method Interpolation

Linear interpolation: Given pass a linear interpolant through the data

where

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Example
Example Interpolation

A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a rectangular plate. The hole centers in the plate that describe the path the arm needs to take are given below.

If the laser is traversing from x = 2 to x = 4.25 in a linear path, find the value of y at x = 4 using the Newton’s Divided Difference method for linear interpolation.

Figure 2 Location of holes on the rectangular plate.

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Linear interpolation
Linear Interpolation Interpolation

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Linear interpolation contd
Linear Interpolation (contd) Interpolation

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Quadratic interpolation
Quadratic Interpolation Interpolation

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Example1
Example Interpolation

A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a rectangular plate. The hole centers in the plate that describe the path the arm needs to take are given below.

If the laser is traversing from x = 2 to x = 4.25 in a linear path, find the value of y at x = 4 using the Newton’s Divided Difference method for quadratic interpolation.

Figure 2 Location of holes on the rectangular plate.

http://numericalmethods.eng.usf.edu


Quadratic Interpolation (contd) Interpolation

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Quadratic interpolation contd
Quadratic Interpolation (contd) Interpolation

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Quadratic interpolation contd1
Quadratic Interpolation (contd) Interpolation

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General form
General Form Interpolation

where

Rewriting

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General form1
General Form Interpolation

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General form2
General form Interpolation

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Example2
Example Interpolation

A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a rectangular plate. The hole centers in the plate that describe the path the arm needs to take are given below.

If the laser is traversing from x = 2 to x = 4.25 in a linear path, find the value of y at x = 4 using the Newton’s Divided Difference method for a fifth order polynomial.

Figure 2 Location of holes on the rectangular plate.

http://numericalmethods.eng.usf.edu


Example3
Example Interpolation

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Example4
Example Interpolation

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Example5
Example Interpolation

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Additional resources
Additional Resources Interpolation

For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, MathCad and MAPLE, blogs, related physical problems, please visit

http://numericalmethods.eng.usf.edu/topics/newton_divided_difference_method.html


THE END Interpolation

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