deletions | additions       diff --git a/section_Solution_approaches__.tex b/Approaches.tex  similarity index 100%  rename from section_Solution_approaches__.tex  rename to Approaches.tex  diff --git a/subsection_General_complex_Prony_N__.tex b/Approaches_General.tex  similarity index 100%  rename from subsection_General_complex_Prony_N__.tex  rename to Approaches_General.tex  diff --git a/subsection_Trigonometric_real_Prony_2D__.tex b/Approaches_Trigonometric.tex  similarity index 100%  rename from subsection_Trigonometric_real_Prony_2D__.tex  rename to Approaches_Trigonometric.tex  diff --git a/Introduction.tex b/Introduction.tex  index 61ee78e..ebb98b0 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
...
Consider the following system of signals:  $$  S = \{ (a_j, x_j) \}, \quad j = 1, \ldots , N $$  where a_j $a_j$  are signals signal  amplitudes and x_j $x_j$  are signals signal  positions. $\{a_j\}$ and $\{x_j\}$ may be represent by real or complex numbers. \par Define the Prony map as a map $\{ (a_j, x_j) \} \mapsto \{m_k\}$ of the following form:  $$  \label{eq:prony}  m_k = \sum_{j=1}^N a_j x_j^k. $$    Numbers  $\{m_k\}$ are moments of the signal system, equation \eqref{eq:prony} is the Prony equation  system. There is a special case of the Prony system:  $$  S_t = \{ (a_j, \mu_j) \}; \quad m_k = \sum_{j=1}^N a_j e^{-2\pi i \mu_j k \delta} $$  where $\delta \in \mathbb{R}_+$ is a parameter. We say that it is the trigonometric Prony map. If $|x_j| = 1$, we can reduce general Prony map to the trigonometric case by $x_j = e^{-2\pi i \mu_j \delta}$. 
...
In this technical report, we consider some examples of the direct and inverse Prony map and build corresponding plots. You can also view the source code on the R language for each plot.  See also: \cite{2015arXiv150206932A}, \cite{azais_spike}, \cite{batenkov_numerical_2014}, \cite{batenkov_accurate_2014}, \cite{Bat.Sar.Yom}, \cite{Bat.Yom2}, \cite{Bat.Yom.Sampta13}, \cite{Bat.Yom1}, \cite{candes_towards_2014}, \cite{candes_super-resolution_2013}, \cite{demanet_super-resolution_2013}, \cite{donoho_superresolution_1992}, \cite{Don1}, \cite{duval_exact_2013}, \cite{fernandez-granda_support_2013}, \cite{heckel_super-resolution_2014}, \cite{Lev.Ful}, \cite{liao_music_2014}, \cite{McC}, \cite{Min.Kaw.Min}, \cite{moitra_threshold_2014}, \cite{Ode.Bar.Pis}, \cite{Sle}, \cite{Yom2}, \cite{Yom1}, \cite{Dem.Ngu}, \cite{Mor.Can}. diff --git a/section_Numerical_examples__.tex b/Numerical.tex  similarity index 100%  rename from section_Numerical_examples__.tex  rename to Numerical.tex  diff --git a/Prony 1D.tex b/Numerical_Prony1D_GeneralReal.tex  similarity index 100%  rename from Prony 1D.tex  rename to Numerical_Prony1D_GeneralReal.tex  diff --git a/Prony 2D.tex b/Numerical_Prony2D_TrigonometricReal.tex  similarity index 100%  rename from Prony 2D.tex  rename to Numerical_Prony2D_TrigonometricReal.tex  diff --git a/In_fact_here_you_can__.tex b/Numerical_Prony2D_TrigonometricReal2.tex  similarity index 100%  rename from In_fact_here_you_can__.tex  rename to Numerical_Prony2D_TrigonometricReal2.tex  diff --git a/subsection_Trigonometric_noisy_real_Prony__.tex b/Numerical_Prony2D_TrigonometricRealNoisy.tex  similarity index 100%  rename from subsection_Trigonometric_noisy_real_Prony__.tex  rename to Numerical_Prony2D_TrigonometricRealNoisy.tex  diff --git a/layout.md b/layout.md  index 871fd2e..9e812db 100644  --- a/layout.md  +++ b/layout.md 
...
Introduction.tex  section_Solution_approaches__.tex  subsection_General_complex_Prony_N__.tex  subsection_Trigonometric_real_Prony_2D__.tex  section_Numerical_examples__.tex  Prony 1D.tex Approaches.tex  Approaches_General.tex  Approaches_Trigonometric.tex  Numerical.tex  Numerical_Prony1D_GeneralReal.tex  figures/prony-1d-map/prony-1d-map.png  figures/prony-1d-map-inv/prony-1d-map-inv.png  Prony 2D.tex Numerical_Prony2D_TrigonometricReal.tex  figures/prony-2d-countour3d/prony-2d-countour3d.gif  In_fact_here_you_can__.tex  subsection_Trigonometric_noisy_real_Prony__.tex Numerical_Prony2D_TrigonometricReal2.tex  Numerical_Prony2D_TrigonometricRealNoisy.tex  figures/prony-2d-noisy/prony-2d-noisy.png