... | ... | @@ -75,13 +75,9 @@ the Newton-Raphson iteration becomes |
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\mathbf{J}(\mathbf{x}_{k-1}) \mathbf{\delta x}_k
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= \mathbf{b} - \mathbf{A}(\mathbf{x}_{k-1}) \mathbf{x}_{k-1}
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```
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with
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```math
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\mathbf{J}(\mathbf{x})_{ij}
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with $`\mathbf{J}(\mathbf{x})_{ij}
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= \frac{\partial(\mathbf{A}(\mathbf{x})\mathbf{x})_i}{\partial\mathbf{x}_j}
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= \frac{\partial\mathbf{A}(\mathbf{x})_{ij}}{\partial\mathbf{x}_j} + \mathbf{A}(\mathbf{x})_{ij} .
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```
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Equivalently, one can solve
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= \frac{\partial\mathbf{A}(\mathbf{x})_{ij}}{\partial\mathbf{x}_j} + \mathbf{A}(\mathbf{x})_{ij}`$. Equivalently, one can solve
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```math
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\mathbf{J}(\mathbf{x}_{k-1}) \mathbf{x}_k
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= \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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... | ... | |