... | ... | @@ -92,7 +92,7 @@ The Picard method is a simple fixed point method applied on the equation $`\math |
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For the exact solution, $`\mathbf{F}(\mathbf{x})`$ is zero; i.e. $`\mathbf{A}(\mathbf{x})\mathbf{x}-\mathbf{b} = 0`$ if $`\mathbf{F}(\mathbf{x}) := \mathbf{A}(\mathbf{x}) \mathbf{x} - \mathbf{b}`$.
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In practice, the iterations are stopped if after $`p`$ iterations a sufficiently small value of the residual, in some norm is obtained, e.g.
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In practice, the iterations are stopped if after $`p`$ iterations a sufficiently small value of the residual in some norm is obtained, e.g.
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```math
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||\mathbf{F}(\mathbf{x}_p)|| < \varepsilon_\text{abs} \quad\text{or}\quad
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\frac{||\mathbf{F}(\mathbf{x}_p)||}{||\mathbf{F}(\mathbf{x}_0)||} < \varepsilon_\text{rel} ,
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