File:NewtonHook.f90: Difference between revisions
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To download, click the link above. | To download, click the link above. | ||
<tt>new_x(:)</tt> and <tt>new_fx(:)</tt> need to be allocated the dimension $n$ | Prior to calling the subroutine <tt>newtonhook(...)</tt>, the arrays <tt>new_x(:)</tt> and <tt>new_fx(:)</tt> need to be allocated the dimension $n$. Also <tt>new_x(:)</tt> needs to be assigned the initial guess prior to the call. As the calculation proceeds, the vector <tt>new_x(:)</tt> is updated with improved vectors (smaller <tt>new_f(:)</tt>). |
Revision as of 06:02, 13 December 2016
$ \renewcommand{\vec}[1]{ {\bf #1} } \newcommand{\bnabla}{ \vec{\nabla} } \newcommand{\Rey}{Re} \def\vechat#1{ \hat{ \vec{#1} } } \def\mat#1{#1} $
The method
Implements the Newton-Raphson-Krylov method for solving \[\vec{F}(\vec{x})=\vec{0},\] where $\vec{x}$ and $\vec{F}$ are $n$-vectors, using a Hookstep-Trust-region approach.
For each iteration, $\vec{x}_{i+1} = \vec{x}_i + \vec{\delta x}$, the linear problem \[\left.\frac{\vec{dF}}{\vec{dx}}\right|_{\vec{x}_i}\,\vec{\delta x}=-\vec{F}(\vec{x}_i) \] is solved for the step $\vec{\delta x}$ subject to the condition that it be smaller than some magnitude $\delta$, where $\delta$ is the size of the trust region. This problem is in the form $A\vec{x}=\vec{b}$, where $A$ is an $n\times n$ matrix, and is solved using the Krylov-subspace method, GMRES(m). See File:GMRESm.f90.
The code
To download, click the link above.
Prior to calling the subroutine newtonhook(...), the arrays new_x(:) and new_fx(:) need to be allocated the dimension $n$. Also new_x(:) needs to be assigned the initial guess prior to the call. As the calculation proceeds, the vector new_x(:) is updated with improved vectors (smaller new_f(:)).
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current | 04:50, 26 June 2019 | (6 KB) | Apwillis (talk | contribs) | Minor edits in comments only. |
05:32, 13 December 2016 | (6 KB) | Apwillis (talk | contribs) | == The method == Implements the Newton-Raphson method for solving \[\vec{F}(\vec{x})=\vec{0}\] with a Hookstep-Trust-region approach. At each iteration, the linear problem for the step in $\vec{x}$ is solved subject to the condition that the step be ... |
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