Update Python README

Author: tttapa

pyproject.toml

@@ -1,6 +1,6 @@
 [project]
 name = "hyhound"
-readme = "python/README.md"
+readme = "python/README.rst"
 requires-python = ">=3.9"
 license = "LGPL-3.0-or-later"
 license-files = ["LICENSE"]

python/README.md

@@ -0,0 +1,66 @@
+.. image:: https://img.shields.io/badge/arXiv-Preprint-b31b1b
+   :target: https://arxiv.org/abs/2503.15372v1
+   :alt: arXiv Preprint
+
+.. image:: https://github.com/kul-optec/hyhound/actions/workflows/linux.yml/badge.svg
+   :target: https://github.com/kul-optec/hyhound/actions/workflows/linux.yml
+   :alt: CI: Linux
+
+.. image:: https://img.shields.io/pypi/dm/hyhound?label=PyPI&logo=python
+   :target: https://pypi.org/project/hyhound
+   :alt: PyPI Downloads
+
+
+hyhound
+=======
+
+**Hy**\perbolic **Ho**\useholder transformations for **U**\p- ‘**n**’ **D**\owndating Cholesky factorizations.
+
+
+Purpose
+-------
+
+Given a Cholesky factor :math:`L` of a dense matrix :math:`H`, the
+``hyhound::update_cholesky`` function computes the Cholesky factor
+:math:`\tilde L` of the matrix
+
+.. math::
+
+   \tilde H = \tilde L \tilde L^\top = H + A \Sigma A^\top,
+
+where :math:`H,\tilde H\in\mathbb{R}^{n\times n}` with :math:`H \succ 0`
+and :math:`\tilde H \succ 0`, :math:`A \in \mathbb{R}^{n\times m}`,
+:math:`\Sigma \in \mathbb{R}^{m\times m}` diagonal,
+and :math:`L, \tilde L\in\mathbb{R}^{n\times n}` lower triangular.
+
+Computing :math:`\tilde L` in this way is done in
+:math:`mn^2 + \mathcal{O}(n^2 + mn)` operations rather than the
+:math:`\tfrac16 n^3 + \tfrac12 mn^2 + \mathcal{O}(n^2 + mn)` operations
+required for the explicit evaluation and factorization of :math:`\tilde H`.
+When :math:`m \ll n`, this results in a considerable speedup over full
+factorization, enabling efficient low-rank updates of Cholesky
+factorizations, for use in e.g. iterative algorithms for numerical
+optimization.
+
+Additionally, hyhound includes efficient routines for updating
+factorizations of the Riccati recursion for optimal control problems.
+
+
+Preprint
+--------
+
+The paper describing the algorithms in this repository can be found on arXiv:  
+`https://arxiv.org/abs/2503.15372v1 <https://arxiv.org/abs/2503.15372v1>`_
+
+.. code-block:: bibtex
+
+   @misc{pas_blocked_2025,
+      title = {Blocked {Cholesky} factorization updates of the {Riccati} recursion using hyperbolic {Householder} transformations},
+      url = {http://arxiv.org/abs/2503.15372},
+      doi = {10.48550/arXiv.2503.15372},
+      publisher = {arXiv},
+      author = {Pas, Pieter and Patrinos, Panagiotis},
+      month = mar,
+      year = {2025},
+      note = {Accepted for publication in the Proceedings of CDC 2025}
+   }