See Subject. Is there some general approach on applying it? I believe it's an iterative process. How does one linearize a function in this case? Suppose one does linearize it, how does one achieve the next step? Can someone provide a simple example of it, say, for something like y = a+b*sin(x)+c*x*x or even just y=a+b*x*x*x?
On Nov 10, 4:42 am, "W. eWatson" <wolftra...@invalid.com> wrote:
> See Subject. Is there some general approach on applying it? I believe > it's an iterative process. How does one linearize a function in this > case? Suppose one does linearize it, how does one achieve the next step? > Can someone provide a simple example of it, say, for something like y > = a+b*sin(x)+c*x*x or even just y=a+b*x*x*x?
If by LSQ you mean "least squares", then your examples are not what you want: they are *linear* (as functions of the "unknowns" a, b and c). These are nonlinear in x, but that does not matter. A truly nonlinear least squares problem might, for example, be of the form y = a + b*exp(c*x) or y = a + b*sin(x+c) or y = a*x^b. Here, there is a nonlinear relation between the unknown parameters a, b, c and the observable y. See, eg., http://en.wikipedia.org/wiki/Least_squares or http://www.statsoft.com/TEXTBOOK/stnonlin.html . One of the standard method used in nonlinear least-squares problems is the Levenberg- Marquardt algorithm. Do a Google search for more details.
Ray Vickson wrote: > On Nov 10, 4:42 am, "W. eWatson" <wolftra...@invalid.com> wrote: >> See Subject. Is there some general approach on applying it? I believe >> it's an iterative process. How does one linearize a function in this >> case? Suppose one does linearize it, how does one achieve the next step? >> Can someone provide a simple example of it, say, for something like y >> = a+b*sin(x)+c*x*x or even just y=a+b*x*x*x?
> If by LSQ you mean "least squares", then your examples are not what > you want: they are *linear* (as functions of the "unknowns" a, b and > c). These are nonlinear in x, but that does not matter. A truly > nonlinear least squares problem might, for example, be of the form y = > a + b*exp(c*x) or y = a + b*sin(x+c) or y = a*x^b. Here, there is a > nonlinear relation between the unknown parameters a, b, c and the > observable y. See, eg., http://en.wikipedia.org/wiki/Least_squares or > http://www.statsoft.com/TEXTBOOK/stnonlin.html . One of the standard > method used in nonlinear least-squares problems is the Levenberg- > Marquardt algorithm. Do a Google search for more details.
> R.G. Vickson
Ah, thanks. It's been awhile. Good wiki reference on the iterative method, which is really what I think I'm after.
