@article{wikipedia,
title = "Scripting language",
author = "[1]",
url = {http://en.wikipedia.org/wiki/Scripting_language},
}
@book{kailath1980linear,
title={Linear Systems},
author={Kailath, T.},
isbn={9780135369616},
lccn={79014928},
series={Information and System Sciences Series},
year={1980},
publisher={Prentice-Hall}
}
这是我的 bib 文件，这是我的 latex
\section{Introduction}
The project will consider direct methods for solving linear systems of equations. A number of methods will be investigated. The project will examine methods for solving general linear systems including Gaussian elimination and LU factorisation as well as methods for special linear systems such as the Cholesky and LDL decompositions.
\section{Structure of the thesis}
In this project, we will start from the analysis of linear system using the linear equations and matrix, and then we will enter the general linear system we will start from the first semester this include the method of Gaussian elimination and the LU method also part the end of the semester we will have completed the first two parts and also start working on the third part third is the method chelosky LDL, in the end, at this three-part there will have been completed the report as well include the final presentation of the project.
\section{Aims of the Project}
In this project I will gain on linear systems how they work in real life. I will be examined in methods of resolving tables and various other methods.
\chapter{PROJECT SCOPE}
\section{Brief definition of a linear system}
Linear systems are systems of equations in which the variables are never multiplied with each other but only with constants and then summed up.A Linear systems,also it's a set of collection of linear equations with the same unknowns,which we're trying to define so that they verify all the equations. For example $n$ linear equations in $n$ unknowns $x_1,x_2,...,x_n$.
We also we will use the formula,
$$\sum_{j=1}^n a_{i,j}x_j=b_i,\quad i=1,2,\ldots,n.\cite{poole2005linear}$$
\section{A Historical Background about linear equation}
First we will start to tell some of the important information and dates concerning linear systems.Starting first I will refer to the year in which the first linear has written 300 of the ancient Babylonians who solved 2 equation with 2 unknowns.The Chinese are between 200 with 100 used matrix.The method used is essentially the Gauss method.The Cardan in the book of Ars Magna at 1545 it's been invented the cramer's rules to resolve 2 equations, approaching the concept of determinants.The Cramer to 1750 gives the general rule that he is now known by his name Cramer's rules for the one solution
nxn systems.
\section{Number of solution in Linear equation}
In linear systems can exist two types of solutions.A solution of a linear system is an assignment of values to the variables\quad$x_1,x_2 \ldots x_n$ such that each of the equations is satisfied with type of solution set.
In general a linear system may have:
\begin{enumerate}
\item infinitely solution,
\item unique solution,
\item no solution
\end{enumerate}
\section{Geometric interpretation}
For a linear system equation has to variable $x$ and $y$ each then determinate a
line.Because is a solution to a linear system must satisfy all of the equations,
the solution set is the intersection of these lines, and is hence either a line, a
single point, or the empty set.
For example,in the Cramer's rule has a geometric interpretation that can be considered also a proof or simply giving insight about its geometric nature. These geometric arguments work in general and not only in the case of two equations with two unknowns.Have an example to illustrate, \label{geometriacal example}
\begin{figure}[htp]
\centering
\includegraphics[scale=.6]{pics/geogebra-export}
\caption{geometrical example}
\label{fig:illustration}
\end{figure}
\subsection{Cramer's rule}
In linear algebra, Cramer's rule is an formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the linear system has a unique solution.Cramer’s Rule is a method that uses determinants to solve systems of equations that have the same number of equations as variables.This considers a system of two linear equations in two variables.
Why Cramer's rule is not suitable for solving large linear systems?\\
This is a good question the solution through the rules of the Cramer nation is impossible because the time required to solve a linear equation is long there is no solution in Cramer's rule in large linear systems.
\section{Numerical method}
The Linear System also can be applied with method of solution:
\begin{itemize}
\item Direct method
\item iterative method
\end{itemize}
\paragraph{Direct method}
\vspace{0.8cm}
A direct method are the results in linear systems can be counted after the experience and many operations.In the absence of a path leads to the exact solution of the linear system equation.In practice however, the accumulation of rounding errors combined with possible algorithm instability or system function, using the method can lead to a completely useless solution. Essentially, all direct methods used are variants of the Gauss elimination method.
\textbf{Iterative method}
$x_{1} \quad x_{2} \quad .... \in\mathbb{R}^n$.In the project will not use this method we use the direct method as well.
\cite{wikipedia}
\chapter{General Linear Systems}
\section{Gaussian Elimination}
Gaussian Elimination also known as
Gaussian elimination works following this step
First Steps:
\bibliographystyle{plain}
\bibliography{bibliography}
\end{document}
错误 u 我无法在我的 pdf 上看到我的参考书目，并且他说第 5 页的引用.....未定义，这是错误的。
答案1
你问，
我的代码有什么错误？
一些观察：
由于您没有指定使用哪个文档类（？？其他内容？）以及加载哪些包，因此无法完全确定所有问题。
report我book了解到，您至少加载了以下包：，，amsmath。您可能还会加载引文管理包（？，？）以及或-- 以及其他包。amssymbgraphicxcitenatbiburlxurl您也没有说明您具体做了什么。在首次运行 LaTeX 之后，您是否运行了 BibTeX，然后又运行了两次 LaTeX？如果您运行了 BibTeX，您是否收到任何警告或错误消息？
该文献有说明，但书目条目中
\cite{poole2005linear}没有带关键词的条目。poole2005linear这不是一个彻底的错误，但可能是其他问题的征兆：bib 条目
kailath1980linear未被使用。将条目类型
@article用于wikipedia条目是错误的。@article条目类型只应用于学术期刊上发表的文章。请检查条目类型@misc。条目author的字段wikipedia肯定是错误的；请author = "Wikipedia"尝试一下。该指令
\vspace{0.8cm}已毫无效果如果在指令后立即遇到\paragraph。我不知道为什么\vspace{0.8cm}会这样。如果您需要在分段标题后换行，请不要使用\paragraph（或者，就此而言\subparagraph）。不要使用
$$来启动和终止 LaTeX 文档中的显示数学模式。相反，使用\[和\]。有关为什么不应该使用 的更多信息$$，请参阅帖子为什么\[ ... \]优于$$ ... $$？说明
\label{geometriacal example}似乎不合适？您要标记什么印刷对象？不要使用
\\来强制在文本模式下换行。相反，使用，\par或者更好的是，创建一个全空行。不要使用
...，更不用说....，来创建印刷省略号。相反，使用\dots。并且在适当的地方，在列表中使用逗号；因此，不要写$x_1,x_2 \ldots x_n$；相反，请写$x_1,x_2,\ldots,x_n$。
答案2
好的，谢谢你所有的回答。问题就在这里。ref 无法显示在我的 pdf 中，我把它发给了我的教授，他说没问题，但你不能编译两次或更多次 latex，现在我尝试了这个，问题就在这里，我无法解决这个问题，我不知道为什么。
@book{atkinson1978,
title={An introduction to numerical analysis},
author={Atkinson, K.E.},
isbn={9780471029854},
lccn={78006706},
year={1978},
publisher={Wiley}
}
@book{poole2005,
title={Linear Algebra: A Modern Introduction},
author={Poole, D.},
isbn={9780534998455},
lccn={2004111976},
year={2005},
publisher={Thomson Brooks/Cole}
}
\chapter{Background of the Project}
\section{Introduction}
I will describe an introduction about a linear systems equation\newline Linear systems are systems of equations in which the variables are never multiplied with each other but only with constants and then summed up.A Linear systems,also it's a set of collection of linear equations with the same unknowns,which we're trying to define so that they verify all the equations. For example $n$ linear equations in $n$ unknowns $x_1,x_2,...,x_n$.
We also we will use the formula,
$$\sum_{j=1}^n a_{i,j}x_j=b_i,\quad i=1,2,\ldots,n.\cite{atkinson1978}$$
\section{A Historical Background about linear equation}
First we will start to tell some of the important information and dates concerning linear systems.Starting first I will refer to the year in which the first linear has written 300 of the ancient Babylonians who solved 2 equation with 2 unknowns.The Chinese are between 200 with 100 used matrix.The method used is essentially the Gauss method.The Cardan in the book of Ars Magna at 1545 it's been invented the cramer's rules to resolve 2 equations, approaching the concept of determinants.The Cramer to 1750 gives the general rule that he is now known by his name Cramer's rules for the one solution or a no solution in a linear equation.
\section{Number of solution in Linear equation}
In linear systems can exist two types of solutions.A solution of a linear system is an assignment of values to the variables\quad$x_1,x_2 \ldots x_n$ such that each of the equations is satisfied with type of solution set.
In general a linear system may have:
\begin{enumerate}
\item infinitely solution,
\item unique solution,
\item no solution
\end{enumerate}
\section{Geometric interpretation}
For a linear system equation has to variable $x$ and $y$ each then determinate a
line.Because is a solution to a linear system must satisfy all of the equations,
the solution set is the intersection of these lines, and is hence either a line, a
single point, or the empty set.\newline
For instance,in the Cramer's rule has a geometric interpretation that can be considered also a proof or simply giving insight about its geometric nature. These geometric arguments work in general and not only in the case of two equations with two unknowns.Have an example to illustrate,
\label{geometriacal example}
\begin{figure}[htp]
\centering
\includegraphics[scale=1]{images/geogebra-export}
\caption{geometrical example}
\label{fig:illustration}
\end{figure}
\section{Cramer's rule}
In linear algebra,Cramer's rule is an formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the linear system has a unique solution.Cramer’s Rule is a method that uses determinants to solve systems of equations that have the same number of equations as variables.This consider a system of two linear equations in two variables.
Why cramer's rule is not suitable for solving large linear system?\newline
This is a good question the solution through the rules of the cramer nation is impossible because the time required to solve a linear equations is long there is no solution in cramer's rule in larg linear system.
\section{Method for solving linear Systems equation}
\par Direct Method
A direct method are the results in linear systems can be count after the experience and many operation.In the absence of a path leads to the exact solution of the linear system equation.In practice however, the accumulation of rounding errors combined with possible algorithm instability or system function, using the method can lead to a completely useless solution. Essentially, all the direct methods used are variants of the Gauss elimination method.
\par iterative method
$x_{1} \quad x_{2} \quad .... \in\mathbb{R}^n$.In the following project will not use this method we use the direct method as well for solving linear systems equation.