What is the cost in terms of flops for the computation of $A$ to the power of $p$, where $p$ is a positive integer and $A \in \mathbb R^{n\times n}$ is a symmetric matrix?

  • $\begingroup$ p is a positive integer $\endgroup$ – tchiki tchinka Apr 19 '20 at 10:50
  • $\begingroup$ Welcome to scicomp. Have tried working it out for a small sizes? How many Operatiions do you need for a 2X2 symmetric matrix? If you have done that for a p=1,2,3 then you might be able to guess the underlying rule. What have you tried so far? $\endgroup$ – MPIchael Apr 20 '20 at 12:29
  • $\begingroup$ Is $p$ small or large? $\endgroup$ – Wolfgang Bangerth Apr 20 '20 at 20:43
  • $\begingroup$ p is small but A is a large matrix $\endgroup$ – tchiki tchinka Apr 21 '20 at 14:02

You can do this in $O(n^3)$ floating point operations by diagonalizing the matrix and applying the spectral theorem.

  • $\begingroup$ let's just say that applying the spectral theorem is not an option $\endgroup$ – tchiki tchinka Apr 19 '20 at 9:16
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    $\begingroup$ You should probably edit your question to make it clear what you are looking for? $\endgroup$ – Brian Borchers Apr 19 '20 at 22:16

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