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Fix typos in docs.
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@@ -74,7 +74,7 @@ and the `std::log` functions, so its accuracy is related to the
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accurate implementations of those functions on a given platform.
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When calculating the quantile with a non-zero /position/ parameter
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catastrophic cancellation errors can occur:
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in such cases, only a low /absolute error/ can be guarenteed.
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in such cases, only a low /absolute error/ can be guaranteed.
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[h4 Implementation]
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@@ -241,7 +241,7 @@ when obtaining the derivative than when not. Consequently there is very little
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from a derivative free method, to Newton iteration. However, once you've calculated the first derivative
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the second comes almost for free, consequently the third order methods (Halley) does much the best.
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* Of the two second order methods, Halley does best as would be expected: the Schroder method offers better
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guarentees of ['quadratic] convergence, while Halley relies on a smooth function with a single root to
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guarantees of ['quadratic] convergence, while Halley relies on a smooth function with a single root to
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give ['cubic] convergence. It's not entirely clear why Schroder iteration often does worse than Newton.
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[endsect][/section:elliptic_comparison Comparison of Elliptic Integral Root Finding Algoritghms]
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@@ -93,8 +93,8 @@ used: the test data was computed using
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[h4 Implementation]
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These functions are implemented using the stable three term
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recurrence relations. These relations guarentee low absolute error
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but cannot guarentee low relative error near one of the roots of the
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recurrence relations. These relations guarantee low absolute error
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but cannot guarantee low relative error near one of the roots of the
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polynomials.
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[endsect][/section:beta_function The Beta Function]
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@@ -145,8 +145,8 @@ used: the test data was computed using
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[h4 Implementation]
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These functions are implemented using the stable three term
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recurrence relations. These relations guarentee low absolute error
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but cannot guarentee low relative error near one of the roots of the
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recurrence relations. These relations guarantee low absolute error
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but cannot guarantee low relative error near one of the roots of the
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polynomials.
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[endsect][/section:beta_function The Beta Function]
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@@ -214,8 +214,8 @@ used: the test data was computed using
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[h4 Implementation]
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These functions are implemented using the stable three term
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recurrence relations. These relations guarentee low absolute error
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but cannot guarentee low relative error near one of the roots of the
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recurrence relations. These relations guarantee low absolute error
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but cannot guarantee low relative error near one of the roots of the
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polynomials.
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[endsect][/section:beta_function The Beta Function]
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