Optimization.TrustRegion.Newton

Newton's method

newton

Arguments

:: (Num a, Ord a, Additive f, Metric f, Foldable f)

=> (f a -> f a)

gradient of function

-> (f a -> f (f a))

inverse Hessian

-> f a

starting point

-> [f a]

iterates

Newton's method

Matrix inversion methods

bicInv :: (Functor m, Distributive m, Additive m, Applicative m, Apply m, Foldable m, Conjugate a) => a -> m (m a) -> [m (m a)]

Inverse by iterative method of Ben-Israel and Cohen starting from alpha A^T. Alpha should be set such that 0 < alpha < 2/sigma^2 where sigma denotes the largest singular value of A

bicInv' :: (Functor m, Distributive m, Additive m, Applicative m, Apply m, Foldable m, Conjugate a) => m (m a) -> m (m a) -> [m (m a)]

Inverse by iterative method of Ben-Israel and Cohen with given starting condition