Reduced complexity of matrix inversion of sum of rank 1 matrices: $M^{-1} = left( I + sum limits_{i=1}^{K}...
How to reduce the complexity of matrix inversion of sum of rank 1 matrices, not only arithmetic but also run time?
$M^{-1} = left( I + sum limits_{i=1}^{K} alpha_i A_i right)^{-1} $
where $A_i in mathbb{C}^{N times N}$, ${rm rank}left(A_i right) = 1$, and $alpha_i in mathbb{R}$.
For instance, the suggestion here is apprently reducing the arithmetic complexity but not the run time (I mean it will take $N$ iterations to find the matrix inverse)? What other alternatives do we have?
linear-algebra computational-complexity numerical-linear-algebra
asked Nov 28 '18 at 12:00
learning
346
add a comment |
How to reduce the complexity of matrix inversion of sum of rank 1 matrices, not only arithmetic but also run time?
$M^{-1} = left( I + sum limits_{i=1}^{K} alpha_i A_i right)^{-1} $
where $A_i in mathbb{C}^{N times N}$, ${rm rank}left(A_i right) = 1$, and $alpha_i in mathbb{R}$.
For instance, the suggestion here is apprently reducing the arithmetic complexity but not the run time (I mean it will take $N$ iterations to find the matrix inverse)? What other alternatives do we have?
linear-algebra computational-complexity numerical-linear-algebra
asked Nov 28 '18 at 12:00
learning
346
add a comment |
How to reduce the complexity of matrix inversion of sum of rank 1 matrices, not only arithmetic but also run time?
$M^{-1} = left( I + sum limits_{i=1}^{K} alpha_i A_i right)^{-1} $
where $A_i in mathbb{C}^{N times N}$, ${rm rank}left(A_i right) = 1$, and $alpha_i in mathbb{R}$.
For instance, the suggestion here is apprently reducing the arithmetic complexity but not the run time (I mean it will take $N$ iterations to find the matrix inverse)? What other alternatives do we have?
linear-algebra computational-complexity numerical-linear-algebra
asked Nov 28 '18 at 12:00
learning
346
How to reduce the complexity of matrix inversion of sum of rank 1 matrices, not only arithmetic but also run time?
$M^{-1} = left( I + sum limits_{i=1}^{K} alpha_i A_i right)^{-1} $
where $A_i in mathbb{C}^{N times N}$, ${rm rank}left(A_i right) = 1$, and $alpha_i in mathbb{R}$.
For instance, the suggestion here is apprently reducing the arithmetic complexity but not the run time (I mean it will take $N$ iterations to find the matrix inverse)? What other alternatives do we have?
linear-algebra computational-complexity numerical-linear-algebra
linear-algebra computational-complexity numerical-linear-algebra
asked Nov 28 '18 at 12:00
learning
346
asked Nov 28 '18 at 12:00
learning
346
asked Nov 28 '18 at 12:00
learning
346
asked Nov 28 '18 at 12:00
learning
346
asked Nov 28 '18 at 12:00
learning
346
346
add a comment |
add a comment |
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