new

diff --git a/mybibfile.bib b/mybibfile.bib
index 47cab483cf0602c7a940815f58477b87ea27301b..5177fd8367c4f48e2dae6e49cc7f974675041fb4 100644 (file)
--- a/mybibfile.bib
+++ b/mybibfile.bib
@@ -165,7 +165,7 @@ OPTannote = {•}
 }
 
 @Article{Kahinall14,
 }
 
 @Article{Kahinall14,

-  title =   "Parallel implementation of the Durand-Kerner algorithm for polynomial root-finding on GPU",
+  title =   "Parallel implementation of the {D}urand-{K}erner algorithm for polynomial root-finding on GPU",

   journal = "IEEE. Conf. on advanced Networking, Distributed Systems and Applications",
   volume =  "",
   number =  "",
   journal = "IEEE. Conf. on advanced Networking, Distributed Systems and Applications",
   volume =  "",
   number =  "",

diff --git a/paper.tex b/paper.tex
index 1d7045055a5a7a4263d6cc3f5659a78c983b1cae..2b6ac7fceebc205ba7f7fa9b2e920153b6501f62 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -350,7 +350,7 @@ iteration function with exponential and logarithm:
 %%$$ \exp \bigl(  \ln(p(z)_{k})-ln(\ln(p(z)_{k}^{'}))- \ln(1- \exp(\ln(p(z)_{k})-ln(\ln(p(z)_{k}^{'})+\ln\sum_{i\neq j}^{n}\frac{1}{z_{k}-z_{j}})$$
 \begin{equation}
 \label{Log_H2}
 %%$$ \exp \bigl(  \ln(p(z)_{k})-ln(\ln(p(z)_{k}^{'}))- \ln(1- \exp(\ln(p(z)_{k})-ln(\ln(p(z)_{k}^{'})+\ln\sum_{i\neq j}^{n}\frac{1}{z_{k}-z_{j}})$$
 \begin{equation}
 \label{Log_H2}

-EA.EL: z^{k+1}=z_{i}^{k}-\exp \left(\ln \left(
+EA.EL: z^{k+1}_{i}=z_{i}^{k}-\exp \left(\ln \left(

 p(z_{i}^{k})\right)-\ln\left(p'(z^{k}_{i})\right)- \ln
 \left(1-Q(z^{k}_{i})\right)\right),
 \end{equation}
 p(z_{i}^{k})\right)-\ln\left(p'(z^{k}_{i})\right)- \ln
 \left(1-Q(z^{k}_{i})\right)\right),
 \end{equation}


@@ -360,7 +360,7 @@ where:
 \begin{equation}
 \label{Log_H1}
 Q(z^{k}_{i})=\exp\left( \ln (p(z^{k}_{i}))-\ln(p'(z^{k}_{i}))+\ln \left(
 \begin{equation}
 \label{Log_H1}
 Q(z^{k}_{i})=\exp\left( \ln (p(z^{k}_{i}))-\ln(p'(z^{k}_{i}))+\ln \left(

-\sum_{k\neq j}^{n}\frac{1}{z^{k}_{i}-z^{k}_{j}}\right)\right).
+\sum_{i\neq j}^{n}\frac{1}{z^{k}_{i}-z^{k}_{j}}\right)\right)i=1,...,n,

 \end{equation}
 
 This solution is applied when the root except the circle unit, represented by the radius $R$ evaluated in C language as:
 \end{equation}
 
 This solution is applied when the root except the circle unit, represented by the radius $R$ evaluated in C language as: