Only author's initials in BibTeX natbib using named style

1. Copy the file named.bst (in TeXLive it is in texmf-dist/bibtex/bst/beebe/named.bst) to the file abbrvnamed.bst in your working directory.

2. Find in this file the line

   FUNCTION {format.names}
   

   and inside the function the line

     { s nameptr "{ff~}{vv~}{ll}{, jj}" format.name$ 't :=
   

3. Change this line to

     { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't :=
   

Now you can put in your document \bibliographystyle{abbrvnamed}, and get the result you want.

For the curious: in this magic line ff means Full First names, f. means abbreviated First names, vv is "Von part", ll is for Last names, jj is for Junior suffix. Yes, BibTeX language is evil.

Now, it's even easier: just use \bibliographystyle{abbrvnat} and it works like a charm.

In my file-containg-bibtex-entries.bib I have the following entry:

@article{Taboada2006,
author = {Taboada, Maite},
doi = {10.1016/j.pragma.2005.09.010},
issn = {03782166},
journal = {Journal of Pragmatics},
keywords = {Coherence relations,Conjunctions,Connectives,Conversation,Discourse markers,Discourse signalling,Newspaper text,RST,Rhetorical Structure Theory},
month = apr,
number = {4},
pages = {567--592},
title = {{Discourse markers as signals (or not) of rhetorical relations}},
url = {http://www.sciencedirect.com/science/article/pii/S0378216605002249},
volume = {38},
year = {2006}
}

My tex file is the following:

%preamble
...
\usepackage{natbib}
...
\begin{document}
According to \cite{Taboada2006}.

\bibliographystyle{abbrvnat}
\bibliography{file-containing-bibtex-entries}

\end{document}

This is what I get: