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Replace broken umalut-o with oe (Ersatzschreibung)

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Matt Borland
2024-08-30 16:14:06 -04:00
parent e6db32aa0a
commit 2def550bfe
1 changed files with 6 additions and 6 deletions
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doc/roots/roots.qbk
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@@ -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 <class F, class T>
T halley_iterate(F f, T guess, T min, T max, int digits, std::uintmax_t& max_iter);
// Schr'''&#xf6;'''der
// Schroeder
template <class F, class T>
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'''&#xf6;'''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'''&#xf6;'''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'''&#xf6;'''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'''&#xf6;'''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: