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In order to find the altitude of a surface, we use the following method.

My question is: What is the name of this method?

We have

$$ A=\begin{pmatrix} a_{1,1} & .. & .. & a_{1,n}&1&x_{1}&y_{1}\\ .. & .. & .. & ..&1&x_{2}&y_{2}\\ .. & .. &.. &.. &1&..&..\\ a_{n,1} &.. &.. &a_{n,n}&1&..&..\\ 1&1&1&1&0&0&0\\ x_{1}&x_{2}&..&..&..&0&0\\ y_{1}&y_{2}&..&..&..&0&0\\ \end{pmatrix} $$ $$z=\begin{pmatrix} z_{1}\\ ..\\ ..\\ z_{n}\\ 0\\ ..\\ 0 \end{pmatrix} $$ Where $a_{i,j}$ is the distance between the point $i$ and the point $j$. $(x_{i},y_{i},z_{i})$ are the coordinates of the point $i$.

We calculate $L=A^{-1}z$

After that, we build the matrix $B$:

$$B=\begin{pmatrix} b_{1,1} & .. & .. & b_{1,n}&1&x'_{1}&y'_{1}\\ .. & .. & .. & ..&1&x'_{2}&y'_{2}\\ .. & .. &.. &.. &1&..&..\\ b_{m,1} &.. &.. &b_{m,n}&1&..&..\\ 1&1&1&1&0&0&0\\ x_{1}&x_{2}&..&..&..&0&0\\ y_{1}&y_{2}&..&..&..&0&0\\ \end{pmatrix} $$ Where $b_{i,j}$ is the distance between the point $i$ we want to calculate the altitude and the measuring point $j$. $(x'_{i},y'_{i},z'_{i})$ are the coordinates of the point $i$ we want to calculate the altitude.

finally,our unknown $z'$ is given by : $z'=BL$ where:$$ z'=\begin{pmatrix} z'_{1}\\ ..\\ ..\\ z'_{n}\\ ..\\ .. \end{pmatrix} $$ Thank you.

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