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The curve fitting problem: A solution. (English) Zbl 0723.65007

Much of scientific inference involves fitting numerical data with a curve. The best fitting curve is the curve which best balances the conflicting demands of simplicity and accuracy, where simplicity is measured by the number of parameters in curve.
In this paper, a measure of the instability of equations is presented. The author gives an idea that the fittest curve is the curve which best balances stability and accuracy. This paper also gives a proof that simplicity corresponds to stability for linear regression equation. The author thinks that stability is desirable, because it leads to repeatable experiments.

MSC:

65D10 Numerical smoothing, curve fitting
65F20 Numerical solutions to overdetermined systems, pseudoinverses
65C99 Probabilistic methods, stochastic differential equations
62J05 Linear regression; mixed models
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