Spline Curves
Figure 1:
Fitting with different degrees of the polynomial.
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- There are times when fitting an interpolating polynomial to data points is very difficult.
- Figure 1a is plot of
on the interval .
- It is a nice, smooth curve but has a pronounced maximum at and is near to the -axis for .
- The curves of Figure 1b,c, d, and e are for polynomials of degrees and that match the function at evenly spaced points.
- None of the polynomials is a good representation of the function.
Figure 2:
Fitting with quadratic in subinterval.
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- One might think that a solution to the problem would be to break up the interval into subintervals
- and fit separate polynomials to the function in these smaller intervals.
- Figure 2 shows a much better fit if we use a quadratic between and , with outside that interval.
- That is better but there are discontinuities in the slope where the separate polynomials join.
- This solution is known as spline curves.
Subsections
Cem Ozdogan
2010-12-06