From 2def550bfe3484d258646f7c27d5052e8fa67261 Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Fri, 30 Aug 2024 16:14:06 -0400 Subject: [PATCH] Replace broken umalut-o with oe (Ersatzschreibung) --- doc/roots/roots.qbk | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/doc/roots/roots.qbk b/doc/roots/roots.qbk index ee3619f4f..ea347639b 100644 --- a/doc/roots/roots.qbk +++ b/doc/roots/roots.qbk @@ -1,4 +1,4 @@ -[section:roots_deriv Root Finding With Derivatives: Newton-Raphson, Halley & Schr'''ö'''der] +[section:roots_deriv Root Finding With Derivatives: Newton-Raphson, Halley & Schroeder] [h4 Synopsis] @@ -22,7 +22,7 @@ template T halley_iterate(F f, T guess, T min, T max, int digits, std::uintmax_t& max_iter); - // Schr'''ö'''der + // Schroeder template T schroder_iterate(F f, T guess, T min, T max, int digits); @@ -61,7 +61,7 @@ For second-order iterative method ([@http://en.wikipedia.org/wiki/Newton_Raphson For the third-order methods ([@http://en.wikipedia.org/wiki/Halley%27s_method Halley] and -Schr'''ö'''der) +Schroeder) the `tuple` should have [*three] elements containing the evaluation of the function and its first and second derivatives.]] [[T guess] [The initial starting value. A good guess is crucial to quick convergence!]] @@ -147,7 +147,7 @@ Out of bounds steps revert to bisection of the current bounds. Under ideal conditions, the number of correct digits trebles with each iteration. -[h4:schroder Schr'''ö'''der's Method] +[h4:schroder Schroeder's Method] Given an initial guess x0 the subsequent values are computed using: @@ -162,8 +162,8 @@ Out of bounds steps revert to __bisection_wikipedia of the current bounds. Under ideal conditions, the number of correct digits trebles with each iteration. -This is Schr'''ö'''der's general result (equation 18 from [@http://drum.lib.umd.edu/handle/1903/577 Stewart, G. W. -"On Infinitely Many Algorithms for Solving Equations." English translation of Schr'''ö'''der's original paper. +This is Schroeder's general result (equation 18 from [@http://drum.lib.umd.edu/handle/1903/577 Stewart, G. W. +"On Infinitely Many Algorithms for Solving Equations." English translation of Schroeder's original paper. College Park, MD: University of Maryland, Institute for Advanced Computer Studies, Department of Computer Science, 1993].) This method guarantees at least quadratic convergence (the same as Newton's method), and is known to work well in the presence of multiple roots: