SecantMethod.hs

-- |
--
-- * [Secant method](https://en.wikipedia.org/wiki/Secant_method)
--
-- * [割線法](https://ja.wikipedia.org/wiki/%E5%89%B2%E7%B7%9A%E6%B3%95)
module SecantMethod where

secantMethod :: (Eq a, Fractional a) => (a -> a) -> a -> a -> [a]
secantMethod f x0 x1 = map fst xs
  where
    xs = (x0, f x0) : (x1, f x1) : zipWith step xs (tail xs)
    
    step (x_prev, fx_prev) (x_curr, fx_curr)
      | fx_curr == fx_prev = (x_curr, fx_curr) -- not necessary converged to a root
      | otherwise = (x_next, fx_next)
      where
        x_next = x_curr - fx_curr * (x_curr - x_prev) / (fx_curr - fx_prev)
        fx_next = f x_next