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Results tagged with nonlinear-equations
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user 28440
Solution of nonlinear systems of equations. The equations might be algebraic or differential equations.
4
votes
1
answer
141
views
Nonlinear least squares when some parameters are linear
Consider the least squares problem,
$$
\min_{\mathbf{a},\mathbf{b}} || \mathbf{f}(\mathbf{a},\mathbf{b})||^2
$$
where $\mathbf{a},\mathbf{b}$ represent the unknown parameters to be found. In my proble …
- 1,078
4
votes
0
answers
350
views
Nonlinear least squares and regularization
Consider the nonlinear least-squares minimization of a vector of $n$ residuals $\mathbf{f}$ in $p$ parameters $\mathbf{x}$:
$$
\min_{\mathbf{x}} || \mathbf{f}(\mathbf{x}) ||^2
$$
This can be done with …
- 1,078
3
votes
1
answer
90
views
Nonlinear least squares resolution matrix
For a linear least squares problem, it is possible to define a resolution matrix, relating the estimated model parameters to the true model parameters. If we are solving a regularized problem,
$$
\min …
- 1,078
1
vote
1
answer
997
views
Pivoted Cholesky vs Modified Cholesky
I am solving nonlinear least squares problems with the normal equations approach, so on each iteration, I need to solve:
$$
J^T J \delta = -J^T f
$$
for the step $\delta$, where $J$ is a large (millio …
- 1,078