\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{read mujprogram2;}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{restart;}{%
\[
\mathit{restart}
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{Digits := 16;}{%
\[
\mathit{Digits} := 16
\]
%
}
\end{maplelatex}

\begin{maplettyout}
Warning, the protected names norm and trace have been redefined and
unprotected
\end{maplettyout}

\begin{maplelatex}
\mapleinline{inert}{2d}{f := x^3+3*x*y+y^3;}{%
\[
f := x^{3} + 3\,x\,y + y^{3}
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{g := exp(x)-2*x+exp(y)-y-3;}{%
\[
g := e^{x} - 2\,x + e^{y} - y - 3
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{fx := 3*x^2+3*y;}{%
\[
\mathit{fx} := 3\,x^{2} + 3\,y
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{fy := 3*x+3*y^2;}{%
\[
\mathit{fy} := 3\,x + 3\,y^{2}
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{gx := exp(x)-2;}{%
\[
\mathit{gx} := e^{x} - 2
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{gy := exp(y)-1;}{%
\[
\mathit{gy} := e^{y} - 1
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{F := vector([x^3+3*x*y+y^3, exp(x)-2*x+exp(y)-y-3]);}{%
\[
F := [x^{3} + 3\,x\,y + y^{3}, \,e^{x} - 2\,x + e^{y} - y - 3]
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{J := matrix([[3*x^2+3*y, 3*x+3*y^2], [exp(x)-2, exp(y)-1]]);}{%
\[
J :=  \left[ 
{\begin{array}{cc}
3\,x^{2} + 3\,y & 3\,x + 3\,y^{2} \\
e^{x} - 2 & e^{y} - 1
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{mujnewton2 := proc (v0::vector) local F0, J0, v1; F0 :=
eval(eval(F),\{x = v0[1], y = v0[2]\}); J0 := eval(eval(J),\{x =
v0[1], y = v0[2]\}); v1 := evalm(v0-linsolve(eval(J0),eval(F0))) end
proc;}{%
\maplemultiline{
\mathit{mujnewton2} := \textbf{proc} (\mathit{v0}\hbox{::}
\mathit{vector}) \\
\textbf{local} \,\mathit{F0}, \,\mathit{J0}, \,\mathit{v1}; \\
\mapleIndent{1} \mathit{F0} := \mathrm{eval}(\mathrm{eval}(F), \,
\{x={\mathit{v0}_{1}}, \,y={\mathit{v0}_{2}}\})\,; \\
\mapleIndent{1} \mathit{J0} := \mathrm{eval}(\mathrm{eval}(J), \,
\{x={\mathit{v0}_{1}}, \,y={\mathit{v0}_{2}}\})\,; \\
\mapleIndent{1} \mathit{v1} := \mathrm{evalm}(\mathit{v0} - 
\mathrm{linsolve}(\mathrm{eval}(\mathit{J0}), \,\mathrm{eval}(
\mathit{F0}))) \\
\textbf{end proc}  }
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{odhad0 := vector([1.6, -.8]);}{%
\[
\mathit{odhad0} := [1.6, \,-0.8]
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{odhad1 := vector([1.605498579860371, -.7662250746521963]);}{%
\[
\mathit{odhad1} := [1.605498579860371, \,-0.7662250746521963]
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{odhad2 := vector([1.605448404509504, -.7658800518916949]);}{%
\[
\mathit{odhad2} := [1.605448404509504, \,-0.7658800518916949]
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{odhad3 := vector([1.605448402044969, -.7658800021965758]);}{%
\[
\mathit{odhad3} := [1.605448402044969, \,-0.7658800021965758]
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{odhad4 := vector([1.605448402044969, -.7658800021965752]);}{%
\[
\mathit{odhad4} := [1.605448402044969, \,-0.7658800021965752]
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{levestrany := vector([-.7e-15, 0.]);}{%
\[
\mathit{levestrany} := [-0.7\,10^{-15}, \,0.]
\]
%
}
\end{maplelatex}

\end{maplegroup}