latex - bold not bold enough in math

Question

I tried to get characters in math-environment bold such that they look like this (picture taken from a book - pdf-sample: link):

However, neither \mathbf{xyz} nor \boldsymbol{\mathrm{xyz}} work in order to get the characters bold enough. In fact it is hard to distinguish bold from non-bold characters. This is the code I tried:

\documentclass[english]{scrartcl}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{textcomp}
\usepackage{amstext}
\usepackage{babel}
\begin{document}
As an application of these results, consider the case in which $\mathbf{X}_{1}$
is $\mathbf{i}$, a constant term that is a column of 1s in the first
column of $\mathbf{X}$. The solution for $b_{2}$ in this case will
then be the slopes in a regression that contains a constant term.
Using Theorem 3.2 the vector of residuals for any variable in $\mathbf{X}_{2}$
in this case will be

$\mathbf{x\text{\textasteriskcentered}}=\mathbf{x}-\mathbf{X}_{1}(\mathbf{X}_{1}'\mathbf{X}_{1})^{-1}\mathbf{X}_{1}\mathbf{x}$

$\textrm{x\text{\textasteriskcentered}}=\textrm{x}-\textrm{X}_{1}(\textrm{X}_{1}'\textrm{X}_{1})^{-1}\textrm{X}_{1}\textrm{x}$ 
\end{document}

Is there a trick how one can get "extra-bold" characters?

BR Fabian

PS: I've tried pretty much all proposals on how to get characters bold that I've found on the internet.

Answer 1

How much contrast exists between the bold and medium font is an aspect of the font design. You haven't given an example document. the default Computer modern has reasonable contrast between the bold and medium weight (which is easy as the medium weight cm is very light)

\documentclass{article}
\usepackage{amsmath}

\begin{document}

$\mathbf{x}\text{\textasteriskcentered}=\mathbf{x}-\mathbf{X}_{1}(\mathbf{X}_{1}^{'}\mathbf{X}_{2}')^{-1}\mathbf{X}'_{1}\mathbf{x}$


$\mathrm{x}\text{\textasteriskcentered}=\mathrm{x}-\mathrm{X}_{1}(\mathrm{X}_{1}^{'}\mathrm{X}_{2}')^{-1}\mathrm{X}'_{1}\mathrm{x}$

\end{document}

Answer 2

The following method only works in pdflatex. I use a pdf special to embolden the font, calling it \mathbbf[]{}. The optional argument allows an optional embolding factor to be specified (default 0.2).

In the MWE, the top line is \mathbbf, the next \mathbf, and the final is \textrm.

\documentclass[english]{scrartcl}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{textcomp}
\usepackage{amstext}
\usepackage{babel}
%%%%%
\usepackage{scalerel,lmodern}
\input pdf-trans
\newbox\qbox
\def\usecolor#1{\csname\string\color@#1\endcsname\space}
\newcommand\outline[1]{\leavevmode%
  \def\maltext{#1}%
  \setbox\qbox=\hbox{\maltext}%
  \boxgs{Q q 2 Tr \thickness\space w 0 0 0 rg 0 G}{}%
  \copy\qbox%
}
\newcommand\mathbbf[2][.2]{%
  \def\thickness{#1}%
  \ThisStyle{\outline{$\mathbf{\SavedStyle#2}$}}%
}
%%%%%
\begin{document}
$\mathbbf{x\text{\textasteriskcentered}}=\mathbbf{x}-\mathbbf{X}_{1}(\mathbbf{X}_{1}'\mathbbf{X}_{1})^{-1}\mathbbf{X}_{1}\mathbbf{x}$

$\mathbf{x\text{\textasteriskcentered}}=\mathbf{x}-\mathbf{X}_{1}(\mathbf{X}_{1}'\mathbf{X}_{1})^{-1}\mathbf{X}_{1}\mathbf{x}$

$\textrm{x\text{\textasteriskcentered}}=\textrm{x}-\textrm{X}_{1}(\textrm{X}_{1}'\textrm{X}_{1})^{-1}\textrm{X}_{1}\textrm{x}$ 
\end{document}

Answer 3

A "dirty" way, which can work if you're using latex outside pdf settings and therefore @Steven's answer can't be directly applied, is to use \pmb{} from the AMSLatex package, on top of the boldface command, possibly nested multiple times.

Below you see v, \bm{v}, \pmb{\bm{v}}, and \pmb{\pmb{\bm{v}}} for the Latex output of LibreOffice's TexMaths extension, with the Palatino-like font from the newpxtext package: