1101011 at gmx.net
Wed Oct 19 17:47:14 CEST 2016
@SE: yes, not every system of equations with more variables than equations is solvable,
we need an additional condition e.g. full rank of the coefficient matrix.
Uniqueness of the solution was not required.
Yes this is the document, it is a nice presentation.
I did not read the first page but note:
Minimizing a sum of squares f(x)=\sum_jf_j(x)^2
is a well defined problem regardless of the number of variables x_i (see f(x)=||x||²).
The condition m>=n really is nonsensical since it can be achieved in any number of ways such as
repeating each residual the same number of times etc. and therefore implies nothing.
What is m>=n supposed to ensure???
Surely not that the matrix Jf(x)'Jf(x) is nonsingular, where Jf denotes the Jacobian of f=(f_1,...,f_m).
Jf(x)'Jf(x) nonsingular, for all x, is a reasonable condition, m>=n is not.
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