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). Then one can find the value of y at any other value of x. This is called Interpolation . Of course, if x falls outside the range of x for which the data is given, it is no longer Interpolation but instead is called extrapolation. So what kind of function xf should one choose?
Newton’s Divided Difference Interpolation 05.03.3 Figure 2 Linear interpolation. Example 1 The upward velocity of a rocket is given as a function of time in Table 1 (Figure 3).
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