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Expressing mathematically the number of real addition operation for a vector after dividing it

The number of additions is just the length of the individual vectors times their number minus $1$: $$\textrm{number of additions}=N\cdot\frac{2^l-1}{2^l}$$ Of course we assume that $N$ is a power of $...
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What is the complexity of multiplication a real matrix with real vector

If you multiply an $M \times N$ matrix with an $N \times 1$ vector you get a vector of size $M \times 1$ For the generic case you will need $M \cdot N$ multiplications and $M \cdot (N-1)$ additions. ...
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How can I express the flipped output of multiplication in function of original inputs?

You just need to conjugate the matrix $D$ as well as the vector $x$, and flip the rows of $D$ upside down, i.e., the first row becomes the last row, etc. I.e., you need to introduce a new matrix $\...
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Finding a good inverse for an ill-conditioned matrix transformation

Simple Answer A simple way to solve this is by using diagonal loading (see this answer for a related example). If your square matrix is $R$, then instead of inverting $R$, invert $R + \sigma I$, where ...
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