Approximations and Interpolations

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SUMMARY

The discussion clarifies the fundamental differences between approximating and interpolating data sets. Interpolation requires that the resulting function passes through all known data points, utilizing methods such as linear interpolation or kriging. In contrast, approximation assumes a specific functional form, such as a polynomial, and aims to minimize error at known points using techniques like least mean square error (LMS). These distinctions are crucial for selecting the appropriate method based on the desired outcome in data analysis.

PREREQUISITES
  • Understanding of interpolation methods, including linear interpolation and kriging.
  • Familiarity with approximation techniques, specifically polynomial fitting.
  • Knowledge of error minimization concepts, particularly least mean square error (LMS).
  • Basic data analysis skills to apply these methods effectively.
NEXT STEPS
  • Research advanced interpolation techniques, focusing on kriging and its applications.
  • Explore polynomial approximation methods and their implementation in data analysis.
  • Study error minimization strategies, particularly in the context of least mean square error (LMS).
  • Learn about the practical applications of interpolation and approximation in real-world data sets.
USEFUL FOR

Data analysts, statisticians, and researchers involved in data modeling and analysis who need to understand the distinctions between approximation and interpolation methods.

pat666
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Hey,
My question is basically what is the difference between approximating and interpolating a data set?

My understanding is that interpolation must pass through every data point while approximations do not need to. Are there any other Fundamental differences?

Thanks
 
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"approximating" will generally assume a functional form eg. ploynomial, then choose coefficients to minimise some definition of error at known points (eg. least mean square error - LMS)

interpolating will use the closest points, and some form of function (eg. linear interpolation) to fill in the values in between the know points, by definition it will use the known values at the known points - another example of an interpolation is kriging
 

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