Re: ? not enough eqns

Cosine wrote :

On Dec 22, 11:24 am, Ray Vickson <RGVick...@xxxxxxx>
wrote:
On Dec 21, 8:39 pm, Cheng Cosine
<asec...@xxxxxxxxx> wrote:

Hi:

 Suppose x belongs to R^n and b belongs to R^m,
and f maps x to b.

When f is a linear map and m < n, we have a
unique approximate of

x in this case as x = trans(f)*inv( f*trans(f)
)*b, trans(f) denotes
the

This approximation is not unique; it is the
"unweighted least squares
deviation" estimate. Other estimates would be
obtained by using a
weighted form of least squares, or by using a total
(weighted or
unweighted) absolute deviation measure, or by using
a minimax absolute
deviation.

R.G. Vickson





transpose of f.

 But what about the case when f is a nonlinear
map? How do we

define a unique approximate as the extension of
the linear case?

  Thanks,- Hide quoted text -

- Show quoted text -

On Dec 22, 11:24 am, Ray Vickson <RGVick...@xxxxxxx>
wrote:
On Dec 21, 8:39 pm, Cheng Cosine
<asec...@xxxxxxxxx> wrote:

Hi:

Suppose x belongs to R^n and b belongs to R^m,
and f maps x to b.

When f is a linear map and m < n, we have a
unique approximate of

x in this case as x = trans(f)*inv( f*trans(f)
)*b, trans(f) denotes
the

This approximation is not unique; it is the
"unweighted least squares
deviation" estimate. Other estimates would be
obtained by using a
weighted form of least squares, or by using a total
(weighted or
unweighted) absolute deviation measure, or by using
a minimax absolute
deviation.

R.G. Vickson





transpose of f.

But what about the case when f is a nonlinear
map? How do we

define a unique approximate as the extension of
the linear case?

Thanks,- Hide quoted text -

- Show quoted text -

Hmm, then how to make sure the solution to each given
approximation

method be unique?

When the map is linear the approximation method I
I placed in my

previous post gives a unique solution. But what if
the map is

nonlinear?

Thanks,


for exact solutions , use the so-called tommy-division.

( yes , my invented tommy-devision posted on sci.math )
.

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