Transcription of Chapter 05.03 Newton’s Divided Difference Interpolation
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Chapter 05.03 Newton’s Divided Difference Interpolation
Chapter Newton s Divided Difference Interpolation After reading this Chapter , you should be able to: 1. derive Newton s Divided Difference method of Interpolation , 2. apply Newton s Divided Difference method of Interpolation , and 3. apply Newton s Divided Difference method interpolants to find derivatives and integrals. What is Interpolation ? Many times, data is given only at discrete points such as ,,00yx 11,yx, .., 11, nnyx, nnyx,. So, how then does one find the value of y at any other value of x? Well, a continuous function xf may be used to represent the 1 n data values with xf passing through the 1 n points (Figure 1).
One of the methods of interpolation is called Newton’s divided difference polynomial method. Other methods include the direct method and the Lagrangian interpolation method. We will discuss Newton’s divided difference polynomial method in ... Note that ,b0 b1, and b2 are finite divided differences. ,b0 b1, and b2 are the first, second,
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