From: Martin Kronbichler Date: Thu, 11 Jul 2019 20:14:11 +0000 (+0200) Subject: Fix documentation of Chebyshev iteration X-Git-Tag: v9.2.0-rc1~1384^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=4dbb801b33cf6e4035f1687085d2ef6bf3f32eba;p=dealii.git Fix documentation of Chebyshev iteration --- diff --git a/include/deal.II/lac/precondition.h b/include/deal.II/lac/precondition.h index b840a8087d..a080971355 100644 --- a/include/deal.II/lac/precondition.h +++ b/include/deal.II/lac/precondition.h @@ -879,7 +879,7 @@ private: * 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). * @f] - * where the parameter $\rho_0$ is set to $\rho_0 = + * where the parameter $\rho_0$ is set to $\rho_0 = 2 * \frac{\lambda_{\max{}}-\lambda_{\min{}}}{\lambda_{\max{}}+\lambda_{\min{}}}$ * for the maximal eigenvalue $\lambda_{\max{}}$ and updated via $\rho_n = * \left(2\frac{\lambda_{\max{}}+\lambda_{\min{}}} @@ -910,9 +910,9 @@ private: * * The Chebyshev method relies on an estimate of the eigenvalues of the matrix * which are computed during the first invocation of vmult(). The algorithm - * invokes a conjugate gradient solver so symmetry and positive definiteness - * of the (preconditioned) matrix system are requirements. The eigenvalue - * algorithm can be controlled by + * invokes a conjugate gradient solver (i.e., Lanczos iteration) so symmetry + * and positive definiteness of the (preconditioned) matrix system are + * requirements. The eigenvalue algorithm can be controlled by * PreconditionChebyshev::AdditionalData::eig_cg_n_iterations specifying how * many iterations should be performed. The iterations are started from an * initial vector that depends on the vector type. For the classes