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I Linearization with Polynomials

  1. May 10, 2017 #1
    Hi everyone.

    I started to look at different linearization techniques like:

    -linear interpolation
    - spline interpolation
    - curve fitting....

    Now Iam wondering (and I guess its very stupid) : As polynomials with a degree > 1 are not linear, why can I use them for linearization?

    With the method of piecewise linear interpolation its clear. You connect two datapoints with a linear function.

    But what about quadratic and cubic splines which are not linear?

    Thanks in advance for any help,

    Kind regards,

    Mike
     
  2. jcsd
  3. May 10, 2017 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hi,

    Can you give an example where someone claims an interpolation by means of a cubic spline or a polynomial is a linear interpolation ?
     
  4. May 10, 2017 #3
    Hi and thanks for your reply.

    Iam trying to learn more about how to linearize outputs of a nonlinear sensor and I found a list in a Master thesis on the web which desribes different techniques for linearization.
    The list says "Piecewise polynomial or spline interpolation"....

    Or is linearization of nonlinear sensors is done with linear polynomials only?

    Regards,

    Mike
     
  5. May 10, 2017 #4
    Hi again.

    I found a section in a scientific paper which mention techniques like:
    - look up table
    - polygonal approximation
    - polynomial approximation
    - cubic spline interpolation

    So I guess that answers one part of my question. Polynomials of higher order can be used?

    But then another question came up.... Whats the difference between plynomial approximation and spline interpolation?

    Thanks again,

    Mike
     
  6. May 10, 2017 #5

    fresh_42

    Staff: Mentor

    I found somewhere ... tell me what is meant, is not an acceptable quotation. So the demand
    is still valid.

    E.g. polynomials could be the elements (points) of the phase space and not the object of the linearization process. In this case, we might talk about a linearization between polynomials of any degree by linear polynomials of polynomials. A bit constructed, I admit, but it shows you the difficulties we face, if you say things like "I have read / found / heard ... somewhere / on the web / in an article".
     
  7. May 10, 2017 #6
    Hi and thanks for your reply!

    Please take into consideration that I have just started with the topic and Iam just confused what is meant by "linearization" of data.... Maybe its the same as interpolation in that context?

    Regards,

    Mike
     
  8. May 11, 2017 #7

    Stephen Tashi

    User Avatar
    Science Advisor

    What context? You haven't revealed the title of the scientific paper or quoted an abstract from it.

    In mathematics, some nouns like "linearization" can be used with a variety of meanings. In spite of the fact that mathematics frowns on ambiguous terminology, mathematics is cultural phenomenon subject to the habits of human beings. So it frowns on ambiguous terminology and also uses it.
     
  9. May 11, 2017 #8
    Hi again.

    As I mentioned earlier I would like to take raw data of a non linear sensor (i.e. a thermocouple) and learn how to linearize these.
    But Iam not sure which techniques are used for that.

    Regards,

    Mike
     
  10. May 11, 2017 #9

    fresh_42

    Staff: Mentor

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