From 55cbe4e374331d6cffc86b67ab838ca0e86065b1 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Tue, 6 Sep 2022 18:42:53 -0400
Subject: [PATCH] fix \tfrac in preconditioners.jl

---
 docs/src/preconditioners.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/docs/src/preconditioners.md b/docs/src/preconditioners.md
index 1bc9b1a7f..7f3fb931e 100644
--- a/docs/src/preconditioners.md
+++ b/docs/src/preconditioners.md
@@ -64,10 +64,10 @@ Methods concerned: [`CGLS`](@ref cgls), [`CRLS`](@ref crls), [`LSLQ`](@ref lslq)
 
 [`LSLQ`](@ref lslq), [`LSQR`](@ref lsqr) and [`LSMR`](@ref lsmr) also handle regularized least-squares problems.
 
-| Formulation           | Without preconditioning                                                    | With preconditioning                                                              |
-|:---------------------:|:--------------------------------------------------------------------------:|:---------------------------------------------------------------------------------:|
-| least-squares problem | $\min \tfrac{1}{2} \\|b - Ax\\|^2_2 + \\tfrac{1}{2} \lambda^2 \\|x\\|^2_2$ | $\min \tfrac{1}{2} \\|b - Ax\\|^2_{E^{-1}} + \\tfrac{1}{2} \lambda^2 \\|x\\|^2_F$ |
-| Normal equation       | $(A^TA + \lambda^2 I)x = A^Tb$                                             | $(A^TE^{-1}A + \lambda^2 F)x = A^TE^{-1}b$                                        |
+| Formulation           | Without preconditioning                                                   | With preconditioning                                                             |
+|:---------------------:|:-------------------------------------------------------------------------:|:--------------------------------------------------------------------------------:|
+| least-squares problem | $\min \tfrac{1}{2} \\|b - Ax\\|^2_2 + \tfrac{1}{2} \lambda^2 \\|x\\|^2_2$ | $\min \tfrac{1}{2} \\|b - Ax\\|^2_{E^{-1}} + \tfrac{1}{2} \lambda^2 \\|x\\|^2_F$ |
+| Normal equation       | $(A^TA + \lambda^2 I)x = A^Tb$                                            | $(A^TE^{-1}A + \lambda^2 F)x = A^TE^{-1}b$                                       |
 | Augmented system      | $\begin{bmatrix} I & A \\ A^T & -\lambda^2 I \end{bmatrix} \begin{bmatrix} r \\ x \end{bmatrix} = \begin{bmatrix} b \\ 0 \end{bmatrix}$ | $\begin{bmatrix} E & A \\ A^T & -\lambda^2 F \end{bmatrix} \begin{bmatrix} r \\ x \end{bmatrix} = \begin{bmatrix} b \\ 0 \end{bmatrix}$ |
 
 | Preconditioners | $E^{-1}$                | $E$                  | $F^{-1}$                | $F$                  |