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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Math-Polynomial-Interpolation.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">polynomial-0.7.2: Polynomials</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>None</td></tr><tr><th>Language</th><td>Haskell98</td></tr></table><p class="caption">Math.Polynomial.Interpolation</p></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><a href="#v:polyInterp">polyInterp</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a => [(a, a)] -> a -> a</li><li class="src short"><a href="#v:neville">neville</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a => [(a, a)] -> a -> [[a]]</li><li class="src short"><a href="#v:nevilleDiffs">nevilleDiffs</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a => [(a, a)] -> a -> [[(a, a)]]</li><li class="src short"><a href="#v:iterativePolyFit">iterativePolyFit</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [(a, a)] -> <a href="Math-Polynomial-Type.html#t:Poly">Poly</a> a</li><li class="src short"><a href="#v:lagrangePolyFit">lagrangePolyFit</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [(a, a)] -> <a href="Math-Polynomial-Type.html#t:Poly">Poly</a> a</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><a id="v:polyInterp" class="def">polyInterp</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a => [(a, a)] -> a -> a <a href="src/Math-Polynomial-Interpolation.html#polyInterp" class="link">Source</a> <a href="#v:polyInterp" class="selflink">#</a></p><div class="doc"><p>Evaluate a polynomial passing through the specified set of points. The
order of the interpolating polynomial will (at most) be one less than
the number of points given.</p></div></div><div class="top"><p class="src"><a id="v:neville" class="def">neville</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a => [(a, a)] -> a -> [[a]] <a href="src/Math-Polynomial-Interpolation.html#neville" class="link">Source</a> <a href="#v:neville" class="selflink">#</a></p><div class="doc"><p>Computes the tableau generated by Neville's algorithm. Each successive
row of the table is a list of interpolants one order higher than the previous,
using a range of input points starting at the same position in the input
list as the interpolant's position in the output list.</p></div></div><div class="top"><p class="src"><a id="v:nevilleDiffs" class="def">nevilleDiffs</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a => [(a, a)] -> a -> [[(a, a)]] <a href="src/Math-Polynomial-Interpolation.html#nevilleDiffs" class="link">Source</a> <a href="#v:nevilleDiffs" class="selflink">#</a></p><div class="doc"><p>Computes the tableau generated by a modified form of Neville's algorithm
described in Numerical Recipes, Ch. 3, Sec. 2, which records the differences
between interpolants at each level. Each pair (c,d) is the amount to add
to the previous level's interpolant at either the same or the subsequent
position (respectively) in order to obtain the new level's interpolant.
Mathematically, either sum yields the same value, but due to numerical
errors they may differ slightly, and some "paths" through the table
may yield more accurate final results than others.</p></div></div><div class="top"><p class="src"><a id="v:iterativePolyFit" class="def">iterativePolyFit</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [(a, a)] -> <a href="Math-Polynomial-Type.html#t:Poly">Poly</a> a <a href="src/Math-Polynomial-Interpolation.html#iterativePolyFit" class="link">Source</a> <a href="#v:iterativePolyFit" class="selflink">#</a></p><div class="doc"><p>Fit a polynomial to a set of points by iteratively evaluating the
interpolated polynomial (using <code><a href="Math-Polynomial-Interpolation.html#v:polyInterp">polyInterp</a></code>) at 0 to establish the
constant coefficient and reducing the polynomial by subtracting that
coefficient from all y's and dividing by their corresponding x's.</p><p>Slower than <code><a href="Math-Polynomial-Interpolation.html#v:lagrangePolyFit">lagrangePolyFit</a></code> but stable under different sets of
conditions.</p><p>Note that computing the coefficients of a fitting polynomial is an
inherently ill-conditioned problem. In most cases it is both faster and
more accurate to use <code><a href="Math-Polynomial-Interpolation.html#v:polyInterp">polyInterp</a></code> or <code><a href="Math-Polynomial-Interpolation.html#v:nevilleDiffs">nevilleDiffs</a></code> instead of evaluating
a fitted polynomial.</p></div></div><div class="top"><p class="src"><a id="v:lagrangePolyFit" class="def">lagrangePolyFit</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [(a, a)] -> <a href="Math-Polynomial-Type.html#t:Poly">Poly</a> a <a href="src/Math-Polynomial-Interpolation.html#lagrangePolyFit" class="link">Source</a> <a href="#v:lagrangePolyFit" class="selflink">#</a></p><div class="doc"><p>Fit a polynomial to a set of points using barycentric Lagrange polynomials.</p><p>Note that computing the coefficients of a fitting polynomial is an
inherently ill-conditioned problem. In most cases it is both faster and
more accurate to use <code><a href="Math-Polynomial-Interpolation.html#v:polyInterp">polyInterp</a></code> or <code><a href="Math-Polynomial-Interpolation.html#v:nevilleDiffs">nevilleDiffs</a></code> instead of evaluating
a fitted polynomial.</p></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.17.3</p></div></body></html>
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