newton()

***constexpr auto eve::newton ( )

constexprnoexcept

If \((c_i)_{0\le i\le n-1}\) denotes the coefficients of the polynomial by decreasing power order, and \((m_i)_{0\le i\le n-2}\) the nodes, the Newton scheme evaluates the polynom \(p\) at \(x\) using the following formula :

\(\qquad\displaystyle p(x) = (((c_0(x-m_0)+c_1)(x-m_1)+ ... )(x-m_{n-2}) + c_{n-1})\)

Header file

#include <eve/module/math.hpp>

Callable Signatures

namespace eve
{
   // Regular overloads
   constexpr auto newton(floating_value auto x, floating_value auto ... cmi)         noexcept; // 1
   constexpr auto newton(floating_value auto x, eve::coefficients ci
                                                eve::nodes auto ni)                  noexcept; // 2
 
   // Lanes masking
   constexpr auto newton<a href="*any of the above overloads*/" >conditional_expr auto c</a>     noexcept; // 3
   constexpr auto newton[logical_value auto m](*any of the above overloads