Clarify and nuance the statement about the largest collection of Kryl…

…ov methods

paper/paper.bib

@@ -78,3 +78,19 @@ @book{greenbaum-1997
   doi       = {10.1137/1.9781611970937},
   publisher = {SIAM}
 }
+
+@techreport{petsc,
+  author      = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Steven Benson and Jed Brown and Peter Brune and Kris Buschelman and Emil Constantinescu and Lisandro Dalcin and Alp Dener and Victor Eijkhout and Jacob Faibussowitsch and William~D. Gropp and V\'{a}clav Hapla and Tobin Isaac and Pierre Jolivet and Dmitry Karpeev and Dinesh Kaushik and Matthew~G. Knepley and Fande Kong and Scott Kruger and Dave~A. May and Lois Curfman McInnes and Richard Tran Mills and Lawrence Mitchell and Todd Munson and Jose~E. Roman and Karl Rupp and Patrick Sanan and Jason Sarich and Barry~F. Smith and Stefano Zampini and Hong Zhang and Hong Zhang and Junchao Zhang},
+  title       = {{PETSc/TAO} Users Manual},
+  institution = {Argonne National Laboratory},
+  number      = {ANL-21/39 - Revision 3.18},
+  year        = {2022},
+}
+
+@book{MATLAB,
+year = {2022},
+author = {MATLAB},
+title = {version 9.13.0 (R2022b)},
+publisher = {The MathWorks Inc.},
+address = {Natick, Massachusetts}
+}

paper/paper.md

@@ -5,6 +5,7 @@ tags:
   - linear algebra
   - Krylov methods
   - sparse linear systems
+  - GPU computing
 authors:
   - name: Alexis Montoison^[corresponding author]
     orcid: 0000-0002-3403-5450
@@ -15,7 +16,7 @@ authors:
 affiliations:
  - name: GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal, QC, Canada.
    index: 1
-date: 29 July 2022
+date: 29 January 2023
 bibliography: paper.bib
 header-includes: |
   \usepackage{booktabs}
@@ -48,7 +49,8 @@ Contrary to direct methods, which require storing $A$ explicitly, Krylov methods
 The same goes with preconditioners, i.e., transformations that modify a linear system into an equivalent form with favorable spectral properties that may yield faster convergence in finite-precision arithmetic.
 We refer interested readers to [@ipsen-meyer-1998] for an introduction to Krylov methods along with [@greenbaum-1997] and [@saad-2003] for more details.
 
-# Features and Functionalities
+<!-- # Features and Functionalities -->
+# Statement of need
 
 ##  Largest collection of Krylov processes and methods
 
@@ -57,6 +59,8 @@ Krylov.jl aims to provide a unified interface for the largest collection of Kryl
 - \textbf{Krylov processes}: \textsc{Arnoldi}, \textsc{Golub-Kahan}, \textsc{Hermitian Lanczos}, \textsc{Montoison-Orban}, \textsc{Non-Hermitian Lanczos},  \textsc{Saunders-Simon-Yip};
 - \textbf{Krylov methods}: \textsc{Bicgstab}, \textsc{Bilq}, \textsc{Bilqr}, \textsc{Cg}, \textsc{Cg-lanczos}, \textsc{Cg-lanczos-shift}, \textsc{Cgls}, \textsc{Cgne}, \textsc{Cgs}, \textsc{Cr}, \textsc{Craig}, \textsc{Craigmr}, \textsc{Crls}, \textsc{Crmr}, \textsc{Diom}, \textsc{Dqgmres}, \textsc{Fgmres}, \textsc{Fom}, \textsc{Gmres}, \textsc{Gpmr}, \textsc{Lnlq}, \textsc{Lslq}, \textsc{Lsmr}, \textsc{Lsqr}, \textsc{Minres}, \textsc{Minres-qlp}, \textsc{Qmr}, \textsc{Symmlq}, \textsc{Tricg}, \textsc{Trilqr}, \textsc{Trimr}, \textsc{Usymlq}, \textsc{Usymqr}.
 
+MATLAB [@MATLAB] and PETSc [@petsc] have nineteen and eighteen distinct Krylov methods, respectively.
+Note that we only consider the number of Krylov methods that generate different iterates.
 Some processes and methods are not available elsewhere and are the product of our own research.
 References for each process and method are available in the extensive [documentation](https://juliasmoothoptimizers.github.io/Krylov.jl/stable/).