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<title>Divided Difference Representation of Polynomials - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">6.2 Divided Difference Representation of Polynomials</h3>
<p><a name="index-divided-differences_002c-polynomials-223"></a><a name="index-evaluation-of-polynomials_002c-in-divided-difference-form-224"></a>
The functions described here manipulate polynomials stored in Newton's
divided-difference representation. The use of divided-differences is
described in Abramowitz & Stegun sections 25.1.4 and 25.2.26.
<div class="defun">
— Function: int <b>gsl_poly_dd_init</b> (<var>double dd</var>[]<var>, const double xa</var>[]<var>, const double ya</var>[]<var>, size_t size</var>)<var><a name="index-gsl_005fpoly_005fdd_005finit-225"></a></var><br>
<blockquote><p>This function computes a divided-difference representation of the
interpolating polynomial for the points (<var>xa</var>, <var>ya</var>) stored in
the arrays <var>xa</var> and <var>ya</var> of length <var>size</var>. On output the
divided-differences of (<var>xa</var>,<var>ya</var>) are stored in the array
<var>dd</var>, also of length <var>size</var>.
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_poly_dd_eval</b> (<var>const double dd</var>[]<var>, const double xa</var>[]<var>, const size_t size, const double x</var>)<var><a name="index-gsl_005fpoly_005fdd_005feval-226"></a></var><br>
<blockquote><p>This function evaluates the polynomial stored in divided-difference form
in the arrays <var>dd</var> and <var>xa</var> of length <var>size</var> at the point
<var>x</var>. An inline version of this function is used when <code>HAVE_INLINE</code> is defined.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_poly_dd_taylor</b> (<var>double c</var>[]<var>, double xp, const double dd</var>[]<var>, const double xa</var>[]<var>, size_t size, double w</var>[])<var><a name="index-gsl_005fpoly_005fdd_005ftaylor-227"></a></var><br>
<blockquote><p>This function converts the divided-difference representation of a
polynomial to a Taylor expansion. The divided-difference representation
is supplied in the arrays <var>dd</var> and <var>xa</var> of length <var>size</var>.
On output the Taylor coefficients of the polynomial expanded about the
point <var>xp</var> are stored in the array <var>c</var> also of length
<var>size</var>. A workspace of length <var>size</var> must be provided in the
array <var>w</var>.
</p></blockquote></div>
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