... | ... | @@ -92,9 +92,9 @@ Equivalently, one can solve |
|
|
|
|
|
### Picard method
|
|
|
|
|
|
When the nonlinear function is of the form $`\mathbf{F}(\mathbf{x}) := \mathbf{A}(\mathbf{x}) \mathbf{x} - \mathbf{b}`$, given an initial guess $`\mathbf{x}_0`$, Picard's method consists in computing the successive iterates $`\mathbf{x}_k`$ such that
|
|
|
When the nonlinear function is of the form $`\mathbf{F}(\mathbf{x}) := \mathbf{A}(\mathbf{x}) \mathbf{x} - \mathbf{b}(\mathbf{x})`$, given an initial guess $`\mathbf{x}_0`$, Picard's method consists in computing the successive iterates $`\mathbf{x}_k`$ such that
|
|
|
```math
|
|
|
\mathbf{A}(\mathbf{x}_{k-1}) \mathbf{x}_k = \mathbf{b},
|
|
|
\mathbf{A}(\mathbf{x}_{k-1}) \mathbf{x}_k = \mathbf{b}(\mathbf{x}_{k-1}),
|
|
|
\quad k = 1, 2, ...
|
|
|
```
|
|
|
|
... | ... | |