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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

1012.0. "Questions on Curve Fitting" by EST::JARGENTATI () Fri Jan 13 1989 16:39

              Hello,

              Perhaps you might have some thoughts on this.

              I have a sequence of non-negative integers which
              have the following properties:

              	1. The sequence is increasing

              	2. No two elements of the sequence are the same

              Some questions:

              I know that a polynomial can be found to fit
              any set of points.  How would the properties of
              this sequence effect the number of terms of the
              polynomial needed to fit it?

              What sorts of curves might fit this data well?

              Any thoughts or suggestions would be greatly
              appreciated.

              Sincerely,
              John Argentati

T.R	Title	User	Personal Name	Date	Lines
1012.1	Well, it ain't going to be easy...	AKQJ10::YARBROUGH	I prefer Pi	`Fri Jan 13 1989 17:50`	12
	In general, a set of N data points requires a polynomial of degree N-1 to fit it exactly. If you can tolerate some error in the fit, a lower-order polynomial might do. If you believe the data points approximate some function, e.g. a Sine function, then a Least Squares fit can be found, i.e. one can find a sinusoidal function that minimizes the sum of the squares of all the "measurement errors". Without knowing anything about the function values, I could not begin to guess what class of functions might be useful in fitting your data. It might be helpful to know what kind of problem you are trying to solve. Lynn Yarbrough
1012.2	More Questions on Curve Fitting	REGENT::PETERS	Chris Peters	`Wed May 03 1989 14:54`	20
1012.3	A low-tech first approach	COOKIE::PBERGH	Peter Bergh, DTN 435-2658	`Thu May 04 1989 11:32`	13
	I suggest that yor first step should be to get yourself some lin-log paper (one axis is linear, the other is logarithmic, a grid is printed on the paper). Plot log(y) against x for the first curve and y against x for the other. If the fit is reasonably close to a straight line for these plots, draw the best lines you can and measure the parameters from your drawing. Least squares does not make a whole lot of sense with only a handful of points; the errors in the estimates will make least squares no better than a hand-drawn line. If it turns out that the fit is no good, try tinkering with some other functions until you get a good fit. Try not to use more than two parameters that describe each curve (again, because of the small number of points).
1012.4	questions about curve fitting	PULSAR::WALLY	Wally Neilsen-Steinhardt	`Thu May 04 1989 17:45`	19
	.1 is still correct. see also 950.24 and some nearby replies. Curve fitting is one of those problems for which there is no best answer. It all depends on where you are going from there. What are you trying to do? optimize a system? analyze a system? approximate some system behavior? interpolate or extrapolate? average out the error? The best curve fitting procedure for your problem depends on the answers to these questions. It is also worth knowing how accurate your point values are, and how expensive the data is.