我使用以下代码在 Latex 中准备海报TeXstudio 2.6.6
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\title{\huge Comparisons of $B_{row}$-splittings of Matrices}
\author{ \vspace{.2cm} {\bf \large{ author}}\\ \vspace{.2cm} Research Supervisor- prof john\\ \vspace{.2cm} School of statistics}
\institute{institute name}
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\begin{minipage}[T]{.95\textwidth} % tweaks the width, makes a new \textwidth
\parbox[t][\columnheight]{\textwidth}{
\begin{block}{INTRODUCTION}
In many practical problems we come across the problem of computing a
solution to a system of linear equations in $n$ unknowns \textcolor{blue}
{\begin{eqnarray}\label{eq0}
Ax=b,\end{eqnarray}
}
where $A$ is a real rectangular $m\times n$ matrix and $b$ is a real $m$-vector.
In a wide variety of such problems, including the Neumann problem and those
for elastic bodies with free surfaces, the finite difference formulations lead to
a singular, consistent linear system (\ref{eq0}) where $A$ is large and sparse.
Here the general method of solution is iterative in nature. Iterative methods
where $A$ is rectangular or inconsistent, have been studied
in \cite{bpcones}. The authors used generalized matrix
inverses for computing least square solutions in the inconsistent
\textcolor{blue}{
\begin{eqnarray}\label{eq01}
x^{(i+1)}=U^{\dag}Vx^{(i)}+U^{\dag}b,
\end{eqnarray}
}
where $U^{\dag}$ is the Moore-Penrose inverse of $U$.
\vspace{.5cm}
The above scheme is said to be convergent if the spectral radius of
$U^{\dag}V$ is less than 1. For a proper splitting, the authors of
\cite{bpcones} have shown that $x=A^{\dag}b$ for any initial
vector $x^{0}$ if and only if (\ref{eq01}) is convergent.
\end{block}
\vfill
\begin{block}{PRELIMINARIES}
\textcolor{darkgreen}{Moore-Penrose inverse}\\
The Moore-Penrose inverse of $A\in {\R}^{m\times n}$
is the unique matrix $A^{\dag}\in {\R}^{n\times m}$ that satisfies the following four
equations:
$$AA^{\dag}A=A,~~~~A^{\dag}AA^{\dag}=A^{\dag},~~~~(AA^{\dag})^{T}=AA^{\dag}~~\mbox{and}
~~(A^{\dag}A)^{T}=A^{\dag}A.$$
If $A^{\dag}\geq 0$, then it is semimonotone. Berman and Plemmons, \cite{bpmonotono}
showed that
$A^{\dag}\geq 0$ if and only if $ Ax\in {\R}^m_+ +N(A^T) ~~\mbox{and}~~x \in
R(A^{T})$ imply $x\geq 0.$
\textcolor{darkgreen}{Row monotone matrix}\\
$A\in {\R}^{m\times n}$ is said to be row monotone \cite{bpmonotono} if $ Ax\geq 0
~~\mbox{and}~~x \in
R(A^{T})$ imply $x\geq 0.$ \\
$A$ is row monotone if and only if $A$ is
$\{1,4\}$-monotone. ($\{1,4\}$-monotone means there is a nonnegative $G$ satisfying
$AGA=A$ and $(GA)^T=GA$.)
If $A^{\dag} \geq 0$, then $A$ and $A^T$ are row monotone.
However, the converse is not true. \\
A decomposition $A=U-V$ of $A\in {\R}^{m\times n}$ is called
\textcolor{blue}{{\it positive}} if $U\geq 0$ and $V\geq 0$. \\
\vspace{.2cm}
\textcolor{darkgreen}{ $B_{row}$-splitting (Definition 2.6, \cite{mis})}\\
A positive proper splitting $A=U-V$ of $A\in {\R}^{m\times n}$ is called a $B_{row}$-
splitting if it satisfies the following conditions: \\
(i) $VU^{\dag}\geq 0$, and \\
(ii) $ Ax,~ Ux\geq 0 ~~\mbox{and}~~x \in R(A^{T})$ imply $x\geq 0.$\\
\vspace{.2cm}
\textcolor{darkgreen}{Theorem 1} (Theorem 2.7, \cite{mis})\\
Let $A\in {\R}^{m\times n}$. Suppose that $R(A) \cap int(\mathbb{R}^m_+) \neq
\emptyset$. Consider the following statements:\\
(a) $A$ is row monotone.\\
(b) $ {\R}_{+}^{m}\cap R(A) \subseteq A{\R}_{+}^{n}$.\\
(c) There exists $x^{0}\in {\R}_{+}^{n}$ such that $Ax^{0} \in int({\R}_{+}^{m})$.\\
Then, we have (a) $\Rightarrow$ (b) $\Rightarrow$ (c).\\
Suppose that $A$ has a $B_{row}$-splitting. Then each of the above is equivalent to the
following:\\
(d) $\rho(VU^{\dag})<1$.
\vspace{.2cm}
\textcolor{darkgreen}{Theorem 2} (Theorem 2.12, \cite{mis})\\
Suppose that $A$ is row monotone and $R(A) \cap int({\R}^{m}_{+}) \neq \emptyset$ for
$A\in {\R}^{m\times n}$.
Further, let $A^{\dag}A\geq 0$. Then $A$ possesses a $B_{row}$-splitting $A=U-V$ with
$\rho(VU^{\dag})<1$.
\end{block}
\vfill
\begin{block}{OBJECTIVE}
To present a more general
convergence theorem for $B_{row}$-splitting and to compare two $B_{row}$-splittings.
\end{block}
}
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\begin{beamercolorbox}[center,wd=\textwidth]{postercolumn}
\begin{minipage}[T]{.95\textwidth} % tweaks the width, makes a new \textwidth
\parbox[t][\columnheight]{\textwidth}{ % must be some better way to set the the height, width and textwidth simultaneously
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\begin{block}{MAIN RESULTS}
We begin with the following lemma which is useful to prove our main results of this section.
\vspace{.4cm}
\textcolor{yellow}{LEMMA 3}\\
\textcolor{blue}{(a) If $A$ is row monotone, $V\geq 0$ and $R(V)\subseteq R(A)$, then
$A^{\dag}V\geq 0$.\\
(b) If $A^T$ is row monotone, $V\geq 0$ and $N(A)\subseteq N(V)$, then $VA^{\dag}\geq
0$.}
\vspace{.4cm}
Now, we obtain a new convergence theorem for $B_{row}$-splittings which holds
even without the assumption $R(A) \cap int({\R}^{m}_{+}) \neq \emptyset$. Thus, the
present one is more general than the earlier one (Theorem 2).
\vspace{.4cm}
\textcolor{yellow}{THEOREM 4}\\
\textcolor{blue}{ Let $A=U-V$ be a $B_{row}$-splitting of $A\in {\R}^{m\times n}$. If
$A$ is row monotone,then\\
(a) $A^{\dag}\geq U^{\dag}$;\\
(b) $\rho(VA^{\dag})\geq \rho(VU^{\dag})$;\\
(c) $\rho(VU^{\dag})=\rho(U^{\dag}V)=\frac{\rho(A^{\dag}V)}{1+\rho(A^{\dag}V)}<1$.}
\vspace{.4cm}
Theorem 2 enables us that there exist several $B_{row}$-splittings of a given matrix.
In this direction, we present two comparison theorems for $B_{row}$-splittings.
\vspace{.4cm}
\textcolor{yellow}{THEOREM 5}\\
\textcolor{blue}{ Let $A=U_{1}-V_{1}=U_{2}-V_{2}$ be two $B_{row}$-splittings of
$A$. If $A$ is row monotone and $V_{2}\geq V_{1}$, then
$$1> \rho(U_{2}^{\dag}V_{2}) \geq \rho(U_{1}^{\dag}V_{1}).$$}
\vspace{.4cm}
\textcolor{yellow}{EXAMPLE 6 }
Let $A=\left(
\begin{array}{cc}
1 & 1 \\
1 & 1 \\
\end{array}
\right)
$. Clearly $A$ is row monotone. Setting
$U_{1}=3A$ and $U_{2}=4A$. We then have $0\leq V_{1}=2A\leq 3A=V_{2}$. Hence
$\rho(V_{1}U_{1}^{\dag})=\frac{2}{3}\leq \frac{3}{4}=\rho(V_{2}U_{2}^{\dag})<1$.
\vspace{.4cm}
The condition $V_2\geq V_1$ can not be dropped. For example, set $V_{1}=3A$ and
$V_{2}=2A$.Then the implication $$\rho(U_{1}^{\dag}V_{1}) \leq \rho(U_{2}^{\dag}V_{2}) <
1$$ does not hold. Similarly,the assumption $U_{1}^{\dag}\geq U_{2}^{\dag}$ in the
Theorem given below can not be dropped.
\vspace{.4cm}
\textcolor{yellow}{THEOREM 7}\\
\textcolor{blue}{ Let $A\in {\R}^{m\times n}$ be such that $A$ and $A^T$ are row
monotone. Let $A=U_{1}-V_{1}=U_{2}-V_{2}$ also be two $B_{row}$-splittings of
$A$. If $U_{1}^{\dag}\geq U_{2}^{\dag}$,then $$1>\rho(U_{2}^{\dag}V_{2}) \geq
\rho(U_{1}^{\dag}V_{1}).$$ }
\end{block}
\vfill
\begin{block}{CONCLUSIONS}
A convergence theorem and comparison theorems for $B_{row}$-splittings are presented.
\end{block}
\vfill
\begin{block}{PUBLICATIONS}
{Jena, L. and Mishra, D.},
\emph{Comparisons of $B_{row}$-splittings and $B_{ran}$-splittings of Matrices},
Linear and Multilinear Algebra, DOI 10.1080/03081087.2012.661426
\end{block}
\vfill
\begin{block}{ACKNOWLEDGEMENTS}
I thank my research supervisor prof. john for his encouragement.
\end{block}
\vfill
\begin{block}{REFERENCES}
\begin{thebibliography}{10}
\bibitem{bpcones} {Berman, A.; Plemmons, R. J.},
\emph{Cones and iterative methods for best square least squares solutions of linear
systems},SIAM J. Numer. Anal., 11 (1974) 145-154.
\bibitem{bpmonotono} {Berman, A.; Plemmons, R. J.},
\emph{Monotonicity and the generalized inverse},SIAM J. Appl. Math. 22 (1972) 155-161.
\bibitem{mis} { Mishra, D.; Sivakumar, K. C.},
\emph{Generalizations of matrix monotonicity and their relationships with
certain subclasses of proper splittings},
Linear Algebra Appl. DOI:10.1016/j.laa.2011.11.016 .
\bibitem{per} {Peris, J. E.},
\emph{A new characterization of inverse-positive matrices},
Linear Algebra Appl. 154/156 (1991) 45-58.
\bibitem{var} {Varga, R. S.},
\emph{Matrix Iterative Analysis}, Springer-Verlag, Berlin, 2000.
\end{thebibliography}
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}
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我收到以下错误
File `deselaers/logos/rwthaachenuniversity-whitegray' not found.
Package xcolor Error: Undefined color `darkgreen' \end{frame}
Package xcolor Error: Undefined color `darkgreen' \end{frame}
Package xcolor Error: Undefined color `darkgreen' \end{frame}
Package xcolor Error: Undefined color `darkgreen' \end{frame}
Package xcolor Error: Undefined color `darkgreen' \end{frame}
File `deselaers/logos/rwthaachenuniversity-whitegray' not found. \end{frame}
我不知道为什么会出现这些错误。我需要专家的帮助。
答案1
确保beamerthemeI6pd2.sty下载最新版本的https://github.com/jtanderson/Fish-Poster/blob/master/beamerthemeI6pd2.sty。
然后将选项传递svgnames给xcolorthrough beamer，这意味着加载beamer为
\documentclass[final,hyperref={pdfpagelabels=false},xcolor={svgnames}]{beamer}
此后，用 替换文档中的所有实例，它应该可以编译darkgreen。DarkGreen
然后您可能需要对文档进行一些调整。
结果如下：
