Newtonâ€™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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Newtonâ€™s Divided Difference Polynomial Method of Interpolation

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Newtonâ€™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

Newtonâ€™s Divided Difference Method of Interpolationhttp://numericalmethods.eng.usf.edu

What is Interpolation ?

Given (x0,y0), (x1,y1), â€¦â€¦ (xn,yn), find the value of â€˜yâ€™ at a value of â€˜xâ€™ that is not given.

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Interpolants

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

Evaluate

Differentiate, and

Integrate.

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Newtonâ€™s Divided Difference Method

Linear interpolation: Given pass a linear interpolant through the data

where

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Example

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 Newtonâ€™s Divided Difference method for linear interpolation.

Figure 2 Location of holes on the rectangular plate.

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Linear Interpolation

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Linear Interpolation (contd)

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Quadratic Interpolation

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Example

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 Newtonâ€™s Divided Difference method for quadratic interpolation.

Figure 2 Location of holes on the rectangular plate.

http://numericalmethods.eng.usf.edu

Quadratic Interpolation (contd)

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Quadratic Interpolation (contd)

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Quadratic Interpolation (contd)

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General Form

where

Rewriting

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General Form

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General form

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Example

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 Newtonâ€™s Divided Difference method for a fifth order polynomial.

Figure 2 Location of holes on the rectangular plate.

http://numericalmethods.eng.usf.edu

Example

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Example

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Example

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Additional Resources

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