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VARPROVariable Projection (algorithm)
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He held 15 patents in electronics, physics, and optics; patents granted worldwide for the Bradford Variable Projection Microscope (BVPM) include the US, Europe, Canada, Mexico, China, Brazil, India, Korea, Taiwan, and Japan.
One particularly useful technique for solving this problem is developed in [4] and involves applying the Gauss-Newton method to the variable projection functional, in essence the norm of [P.sup.[perpendicular to]]y.
[5] --, Separable nonlinear least squares: the variable projection method and its applications, Inverse Problems, 19 (2003), pp.
Kaufman, A variable projection method for solving separable nonlinear least squares problems, BIT, 15 (1975), pp.
One caveat though: the most common eyepiece-projection adapters have only enough room inside them to accommodate ordinary 1 1/4-inch eyepieces--big-body eyepieces will not fit (for these you'll need the new MaxView DSLR Variable Projection Adapter from ScopeTronix).
In [1] a systematic procedure (variable projection) is introduced for reducing the estimation problem to a nonlinear least squares problem in the nonlinear parameters [beta] only.
Variable projection leads to the nonlinear least squares problem (1.5) where
Introducing the variable projection matrix P permits this to be written:
Thus a choice between variable projection and Gauss-Newton must depend on other factors.
The nonlinear parameters can be bounded so it is possible for variable projection to yield a well determined answer.
For some pseudo-multivariate functions whose one variable projection functions have general explicit formulas of Pade approximants, like the ones given in [7], we can use Theorem 1.3 to write their general order multivariate Pade approximants.
In the procedure mpa(f, x, m, n), f is the one variable projection function of the pseudo-multivariate function F, x is the variable of f , m and n are non-negative integers.
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