2

I am curious to know what document class produces the following style in the title and in the section area. Here are some examples:

enter image description here

The placement of the title in addition to the author's name (and font size difference of the title and the author name) in this example seem to be perfectly positioned from some document class. Furthermore, there appears to be another feature in the section where the font style is in \textsc

enter image description here

3
  • 3
    It's amsart. The typesetting is spoiled by \usepackage{times}
    – egreg
    Commented Jul 5, 2022 at 20:15
  • @egreg at least it has serif titles?
    – Skillmon
    Commented Jul 5, 2022 at 20:32
  • 1
    @Skillmon Of course! But the obvious problem is that the math font clashes violently with the text font and that the small caps are painfully faked.
    – egreg
    Commented Jul 5, 2022 at 20:42

1 Answer 1

5

It's definitely amsart. Unfortunately, it uses \usepackage{times} as the following shows

enter image description here

I found the article at https://www.math.uci.edu/~chenlong/226/Ch6IterativeMethod.pdf and copied the introduction. You can see that the output is exactly the same.

\documentclass[a4paper]{amsart}

\usepackage{times}
\usepackage{lipsum}

\begin{document}

\title{Classical iterative methods}
\author{Long Chen}

\maketitle

In this notes we discuss classic iterative methods on solving 
the linear operator equation
\begin{equation}\label{operator-eq}
Au = f,
\end{equation}
posed on a finite dimensional Hilbert space $\mathbb{V}\cong\mathbb{R}^N$ 
equipped with an inner product $(\cdot,\cdot)$. Here 
$A : \mathbb{V}\mapsto \mathbb{V}$ is an \emph{symmetric and positive definite (SPD)} 
operator, $f\in\mathbb{V}$ is given, and we are looking for $u\in\mathbb{V}$ such 
that~\eqref{operator-eq} holds.

The direct method to solve~\eqref{operator-eq} is to form $A^{-1}$ or the action 
of $A^{-1}f$. For example, the Gaussian elimination or LU factorization still 
remains the most commonly used methods in practice. It is a black-box as it can 
be applied to any problem in principle. For general dense matrices, a matrix-vector 
product requires $\mathcal{O}(N^2)$ operations and the straightforward
implementation of Gauss elimination is $\mathcal{O}(N^3)$, which is prohibitive 
large when $N$ is large. The state-of-the-art of direct solvers can achieve the 
nearly linear complexity for certain structured sparse matrices; see for example~[2].

When $A$ is sparse, the nonzero entries of $A$ is $\mathcal{O}(N)$ and the 
basic matrix-vector product reduces to $\mathcal{O}(N)$ operation. Then it is 
desirable to design optimally scaled solvers, say, with $\mathcal{O}(N)$ or 
$\mathcal{O}(N\log N)$ computational cost. Namely computing $A^{-1}f$ is just 
a few number of $Ax$. To this end, we first introduce a basic residual-correction 
iterative method and study classic iterative methods.

To see the huge saving of an $\mathcal{O}(N)$ algorithm comparing with 
an $\mathcal{O}(N^2)$ one when $N$ is large, let us do the following calculation. 
Suppose $N = 10^6$ and a standard PC can do the summation of $10^6$ numbers 
in $1$ minute. Then an $\mathcal{O}(N)$ algorithm will finish in few
minutes while an $\mathcal{O}(N^2)$ algorithm will take nearly two years 
($10^6$ minutes $\approx$ 694 days).

\section{Residual-Correction Method}

\lipsum[1-30]

\end{document}

I added Lipsum text just to produce some more pages and see the headers.

enter image description here

enter image description here

Now, let me change some parts to get better typesetting with a Times clone also for math. Chase for the differences (there might also be some other improvements to make).

\documentclass[a4paper]{amsart}

\usepackage{newtx}
\usepackage[cal=cm,bb=ams]{mathalpha}

\usepackage{lipsum}

\begin{document}

\title{Classical iterative methods}
\author{Long Chen}

\maketitle

In this notes we discuss classic iterative methods on solving 
the linear operator equation
\begin{equation}\label{operator-eq}
Au = f,
\end{equation}
posed on a finite dimensional Hilbert space $\mathbb{V}\cong\mathbb{R}^N$ 
equipped with an inner product $(\cdot,\cdot)$. Here 
$A\colon \mathbb{V}\to \mathbb{V}$ is a \emph{symmetric and positive definite} (SPD) 
operator, $f\in\mathbb{V}$ is given, and we are looking for $u\in\mathbb{V}$ such 
that~\eqref{operator-eq} holds.

The direct method to solve~\eqref{operator-eq} is to form $A^{-1}$ or the action 
of $A^{-1}f$. For example, the Gaussian elimination or LU factorization still 
remains the most commonly used methods in practice. It is a black-box as it can 
be applied to any problem in principle. For general dense matrices, a matrix-vector 
product requires $\mathcal{O}(N^2)$ operations and the straightforward
implementation of Gauss elimination is $\mathcal{O}(N^3)$, which is prohibitive 
large when $N$ is large. The state-of-the-art of direct solvers can achieve the 
nearly linear complexity for certain structured sparse matrices; see for example~[2].

When $A$ is sparse, the nonzero entries of $A$ is $\mathcal{O}(N)$ and the 
basic matrix-vector product reduces to $\mathcal{O}(N)$ operation. Then it is 
desirable to design optimally scaled solvers, say, with $\mathcal{O}(N)$ or 
$\mathcal{O}(N\log N)$ computational cost. Namely computing $A^{-1}f$ is just 
a few number of $Ax$. To this end, we first introduce a basic residual-correction 
iterative method and study classic iterative methods.

To see the huge saving of an $\mathcal{O}(N)$ algorithm comparing with 
an $\mathcal{O}(N^2)$ one when $N$ is large, let us do the following calculation. 
Suppose $N = 10^6$ and a standard PC can do the summation of $10^6$ numbers 
in $1$ minute. Then an $\mathcal{O}(N)$ algorithm will finish in few
minutes while an $\mathcal{O}(N^2)$ algorithm will take nearly two years 
($10^6\,\text{minutes}\approx 694\,\text{days}$).

\section{Residual-Correction Method}

\lipsum[1-30]

\end{document}

enter image description here

1
  • 2
    With all the AMS document classes, article titles and running heads are not small caps; they are "smaller" full caps. The reason is that making math look decent in a small caps environment is nearly impossible. In a single section heading, it can be overlooked, but in oft-repeated running heads, this is simply too obvious to be tolerated. Commented Jul 5, 2022 at 22:57

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .