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

In summary, the conversation is about finding a good approximation for a non-analytic curve using linear algebra and numerical integration. The person is looking for textbooks on linear algebra and seeking help in finding the parameters for the function that best fits the data. They also mention a paper that provides examples involving numerical integration.
  • #1
mikeph
1,235
18
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 dependant 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,
 
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  • #2
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.
 
  • #3
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.
 
  • #4
I suggest you describe your problem completely.
 
  • #5
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
 

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

What is nonlinear curve fitting?

Nonlinear curve fitting is a statistical method used to determine the relationship between two or more variables when the relationship cannot be described by a linear function. It involves finding the best-fit curve that represents the data points, using a mathematical model that may include multiple variables and parameters.

When is nonlinear curve fitting used?

Nonlinear curve fitting is used when there is a suspected nonlinear relationship between variables, or when the data points do not follow a linear pattern. It is commonly used in fields such as physics, biology, economics, and engineering to analyze and model complex data.

What is the difference between linear and nonlinear curve fitting?

The main difference between linear and nonlinear curve fitting is the type of function used to fit the data. Linear curve fitting uses a linear function (e.g. y = mx + b), while nonlinear curve fitting uses a nonlinear function (e.g. y = a + bx^2). Nonlinear curve fitting is more versatile as it can capture more complex relationships between variables.

What factors can affect the accuracy of nonlinear curve fitting?

The accuracy of nonlinear curve fitting can be affected by several factors, including the choice of model and parameters, the quality and quantity of data, and the presence of outliers or errors in the data. It is important to carefully select the appropriate model and to evaluate the goodness of fit to ensure the accuracy of the results.

What are some common methods used for nonlinear curve fitting?

Some common methods used for nonlinear curve fitting include the least squares method, maximum likelihood estimation, and nonlinear regression. Each method has its own advantages and limitations, and the choice of method should be based on the specific data and research goals.

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