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Results tagged with jacobian
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Questions related to the calculation or use of the Jacobian matrix or its determinant. Not to be confused with the Jacobi iterative method for solving systems of linear equations. For those, use [iterative-method] instead.
1
vote
Accepted
Non-linear root finding with positive definite Jacobian
The question changed, so this a new answer. If
$(z,J(x)z)\geq\epsilon>0$, then take (w.l.o.g.) $f(0)=0$, and consider a
path $g:[0,1]\to\mathbb{R}^n$ such that
$$ g(0) = 0, \qquad f(g(0)) = 0, \qquad …
- 11.5k
4
votes
Non-linear root finding with positive definite Jacobian
You could consider $d=1$ and
$$ f(x) = e^x, \qquad y=0. $$
I don't think a function's derivative being positive everywhere implies that the function's range is all of $\mathbb{R}$.
It does imply, tho …
- 11.5k
2
votes
Accepted
Confusion about determining the jacobian in a rootfinding algorithm
The first, ipvt explains what happened to variable ordering—there was a pivoting step when dealing with the Jacobian and when I ran your code, the pivots were $[3,2,1]$, matching the permutation of the … One other thing I noticed is that lmdif doesn't produce the actual Jacobian—note that the field is called fjac (as in lmdif), not jac (as in scipy). …
- 11.5k