From ea0a48ec5885892dc9b9d323b8f75ba0a085fd0f Mon Sep 17 00:00:00 2001 From: Peter Munch Date: Sat, 23 Oct 2021 15:18:03 +0200 Subject: [PATCH] Fix docu of PreconditionChebyshev --- include/deal.II/lac/precondition.h | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) 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{}}} -- 2.39.5