deletions | additions       diff --git a/subsection_Trigonometric_noisy_real_Prony__.tex b/subsection_Trigonometric_noisy_real_Prony__.tex  index 058a1c7..d7a9b17 100644  --- a/subsection_Trigonometric_noisy_real_Prony__.tex  +++ b/subsection_Trigonometric_noisy_real_Prony__.tex 
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\subsection{Trigonometric noisy real Prony, 2D}  General solving approach for general complex Prony problems doesn't work well for noisy system. Consider the following numerical example: we have two-dimensional trigonometry Prony system ($S_1$). Let's add some noise to the moments and try to reconstruct original system by the general approach ($S_2$) and the trigonometry trigonometric  approach ($S_3$). The numerical results are in the table \ref{tbl:noisy}.  \begin{table} 
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& $x_1$ & $x_2$ & $a_1$ & $a_2$ & $m_0$ & $m_1$ & $m_2$ & $m_3$ \\   \hline  $S_1$ & 0.891-0.454i & 0.951-0.309i & 1+0i & 1+0i & 2+0i & 1.84-0.76i & 1.4-1.4i & 0.74-1.8i \\   $S_2$ & 0.919-0.385i & 1.93-6.15i & 2.04+0.09i & 5.17e-04-2.6e-04i 0.0005-0.0002i  & 2.04+0.09i & 1.91-0.71i & 1.46-1.39i & 0.76-1.7i \\ $S_3$ & 0.953-0.304i & 0.916-0.402i & 1.02+0i & 1.02+0i & 2.04+0.09i & 1.91-0.71i & 1.46-1.39i & 0.76-1.7i \\   $S_2-S_1$ & 0.0277+0.0691i & 0.98-5.84i & 1.04+0.09i & -0.999-0i & 0.0425+0.0877i & 0.067+0.0542i & 0.0624+0.0105i & 0.019+0.0951i \\   $S_3-S_1$ & 0.062+0.15i & -0.0355-0.0932i & 0.0222+0i & 0.0222+0i & 0.0425+0.0877i & 0.067+0.0542i & 0.0624+0.0105i & 0.019+0.0951i \\  
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\end{tabular}  \end{table}    We can see that the general approach gives a big error for $x_2$ and $a_2$. The trigonometric approach solves the noisy problem well.