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Inverse of small matrices also numerically stable?

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vernal
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Inverse of small matrices also numerically stable?

Tue May 03, 2011 2:25 pm
The eigen tutorial/docs say:
While certain decompositions, such as PartialPivLU and FullPivLU, offer inverse() and determinant() methods, you can also call inverse() and determinant() directly on a matrix. If your matrix is of a very small fixed size (at most 4x4) this allows Eigen to avoid performing a LU decomposition, and instead use formulas that are more efficient on such small matrices.

Does that mean that it is always advisable/better for matrices smaller than 4x4 to call the .inverse() function instead of performing a decomposition? Are there numerically stable operations performed?

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vernal
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ggael
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Re: Inverse of small matrices also numerically stable?

Wed May 04, 2011 10:02 am
regarding numerical accuracy it is always better not to compute the inverse but directly compute A^1 * B through the solve methods of the decompositions. Now, for very small matrices, specialized inverse functions are also much faster and should give enough accuracy in most cases.

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