From: Peter Munch <peterrmuench@gmail.com>
Date: Sat, 23 Oct 2021 13:18:03 +0000 (+0200)
Subject: Fix docu of PreconditionChebyshev
X-Git-Tag: v9.4.0-rc1~897^2
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=ea0a48ec5885892dc9b9d323b8f75ba0a085fd0f;p=dealii.git

Fix docu of PreconditionChebyshev
---

diff --git a/include/deal.II/lac/precondition.h b/include/deal.II/lac/precondition.h
index f0b8cbe470..2334f5b667 100644
--- a/include/deal.II/lac/precondition.h
+++ b/include/deal.II/lac/precondition.h
@@ -870,10 +870,14 @@ private:
  * @p smoothing_range. The algorithm is based on the following three-term
  * recurrence:
  * @f[
- *  x^{n+1} = x^{n} + \rho_n \rho_{n-1} (x^{n} - x^{n-1}) +
- *     \frac{\rho_n}{\lambda_{\max{}}-\lambda_{\min{}}} P^{-1} (b-Ax^n).
+ *  x^{n+1} = x^{n} + \alpha^n_0 (x^{n} - x^{n-1}) + \alpha^n_1 P^{-1} (b-Ax^n)
+ *    \quad\text{with}\quad
+ *    \alpha^0_0 := 0,\;
+ *    \alpha^0_1 := \frac{2\rho_0}{\lambda_{\max}-\lambda_{\min}}\;
+ *    \alpha^n_0 := \rho_n \rho_{n-1},\;\text{and}\;
+ *    \alpha^n_1 := \frac{4\rho_n}{\lambda_{\max}-\lambda_{\min}},
  * @f]
- * where the parameter $\rho_0$ is set to $\rho_0 = 2
+ * where the parameter $\rho_0$ is set to $\rho_0 =
  * \frac{\lambda_{\max{}}-\lambda_{\min{}}}{\lambda_{\max{}}+\lambda_{\min{}}}$
  * for the maximal eigenvalue $\lambda_{\max{}}$ and updated via $\rho_n =
  * \left(2\frac{\lambda_{\max{}}+\lambda_{\min{}}}