Eta update using Newton's method with backtracking

update_eta_bktk updates the precision parameter tau = e^eta for L2E regression using Newton's method

update_eta_bktk(r, eta, max_iter = 100, tol = 1e-10)

Arguments

r	Vector of residual
eta	Initial estimate of eta
max_iter	Maximum number of iterations
tol	Relative tolerance

Value

Returns a list object containing the new estimate for eta (scalar), the number of iterations (scalar) the update step utilized, the eta and objective function solution paths (vectors), and the first and second derivatives calculated via Newton's method (vectors)