What are some recommended textbooks for learning non-analytic curve fitting?

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Discussion Overview

The discussion centers around recommendations for textbooks focused on non-analytic curve fitting, particularly in the context of fitting known functional forms to data. Participants explore various approaches and techniques relevant to this topic, including numerical integration and linear algebra methods.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks textbooks specifically on non-analytic curve fitting, mentioning a need to learn quickly and the expectation that the fitting process should not be overly complex.
  • Another participant suggests using linear algebra to find the best approximation to data points through a linear combination of functions, referencing general linear algebra textbooks as resources.
  • A participant notes that the function in question involves a numerical integral, indicating that they are looking for parameters that best fit the data despite the complexity of the function.
  • One participant requests a more detailed description of the problem to provide better recommendations.
  • A later reply reiterates the importance of knowing the function and the form of the related integral to give a more relevant answer, mentioning a specific paper that discusses numerical integration.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on specific textbook recommendations, and multiple approaches to the problem are discussed without resolution.

Contextual Notes

The discussion highlights the dependence on the specific form of the function and the integral involved, which may limit the applicability of general recommendations. There are also unresolved aspects regarding the nature of the non-analytic curve fitting process.

mikeph
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Hi,

what are some good textbooks dedicated to this subject? I have a short time to learn everything about this subject (upto a certain level). I'm trying to fit a non-analytic curve (whose form I know) to some data.

edit- sorry, I don't only mean non-linear, I mean non-analytic. The curve is smoothly dependent on the parameter space so I don't expect it to be difficult, but it takes a computer to estimate its value. A human could do better than my current attempt at coding.

Thanks,
 
Last edited:
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You can use linear algebra to find the "best" approximation to a set of data points using a linear combination of different functions. E.g. if you expect that a good approximation could be Ax+Bx^2+Csin(x), you can find constants A,B and C such that this function is optimized wrt your data points. More variables can also be used. This is treated in many books on linear algebra. E.g. Lay's.
 
I know exactly what the function is, but it involves an integral that can only be calculated numerically. I'm seeking the parameters of this awkward function that causes it to best fit the data.
 
I suggest you describe your problem completely.
 
I know exactly what the function is, but it involves an integral that can only be calculated numerically.

If we knew what is the function and the form of the related integral, it might be possible to give a more pertinent answer.
Some examples involving numerical integration are provided in the paper "Régressions et Equations Intégrales" (not translated yet)
http://www.scribd.com/JJacquelin/documents
 

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