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1 results

  • 9 - Base Functions and Linear Independence

  • Chunyan Li, Louisiana State University
  • Book:
    Time Series Data Analysis in Oceanography
    Published online:
    21 April 2022
    Print publication:
    05 May 2022, pp 165-177

  • Summary

    The objective of this chapter is to discuss the concept of base functions and the basics of using some simple base functions to represent other functions. These base functions are needed in many commonly used analyses. An example of using base functions to approximate an almost arbitrary target function is the Taylor series expansion we have discussed. Here we say that an “almost arbitrary function” is not really arbitrary because, in theory, the target function must be differentiable an arbitrary number of times for the Taylor series expansion to be valid. The concept of linear independence of functions is important in understanding the selection of base functions.