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  • Nonlinear solvers

Nonlinear solvers · Changes

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Update Nonlinear solvers authored Apr 24, 2018 by Christophe Geuzaine's avatar Christophe Geuzaine
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Nonlinear-solvers.md
View page @ a0ed61fc
......@@ -75,13 +75,9 @@ the Newton-Raphson iteration becomes
\mathbf{J}(\mathbf{x}_{k-1}) \mathbf{\delta x}_k
= \mathbf{b} - \mathbf{A}(\mathbf{x}_{k-1}) \mathbf{x}_{k-1}
```
with
```math
\mathbf{J}(\mathbf{x})_{ij}
with $`\mathbf{J}(\mathbf{x})_{ij}
= \frac{\partial(\mathbf{A}(\mathbf{x})\mathbf{x})_i}{\partial\mathbf{x}_j}
= \frac{\partial\mathbf{A}(\mathbf{x})_{ij}}{\partial\mathbf{x}_j} + \mathbf{A}(\mathbf{x})_{ij} .
```
Equivalently, one can solve
= \frac{\partial\mathbf{A}(\mathbf{x})_{ij}}{\partial\mathbf{x}_j} + \mathbf{A}(\mathbf{x})_{ij}`$. Equivalently, one can solve
```math
\mathbf{J}(\mathbf{x}_{k-1}) \mathbf{x}_k
= \mathbf{b} - \mathbf{A}(\mathbf{x}_{k-1}) \mathbf{x}_{k-1} + \mathbf{J}(\mathbf{x}_{k-1}) \mathbf{x}_{k-1} .
......
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