[Numpy-discussion] Matrix square root

[Bernard Frankpitt]

Andrew Nesbit wrote:

>Konrad Hinsen <hinsen at cnrs-orleans.fr> writes:
>
>>On Thursday 04 September 2003 16:42, Andrew Nesbit wrote:
>>    
>>
>>>I need a function equivalent to Matlab's sqrtm, i.e., a square root
>>>for matrices
>>>
>[snip]
>
>>I'd use an eigenvalue decomposition, then take the square root of the 
>>eigenvalues, and then apply the diagonlization matrix in reverse. If you 
>>convert to eigenvalues to complex before taking the square root, this will 
>>work for non-positive-definite matrices, yielding a complex result
>>
>
>Thankyou for the advice.  This gives me a good starting point.
>
>Andrew.
>
>  
>
The only problem with this approach is that you have to find all the 
eigenvalues and eigenvectors to get the spectral decomposition.  For 
large, poorly conditioned matrices this can be a source of significant 
errors, and a lot of work. An alternative, and often faster and more 
accurate approach is to use a series expansion for the square root. 
Evaluating the series expansion only requires multiplication.

Bernie