5e818d2f-2866-4b3a-a599-b96219c80f73 14 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

References:

http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method

β:Polak–Ribière

Nonlinear conjugate gradient method. 1 f x.0 ε maxIters NCGM.ref m x.0 f rows eval : x# F 12 / x# f i el (2^(i 1 m sum * : k 0 : x x.0 : h.SD x# F x Gradient - eval : α x α# h.SD * + F 010102 -^GoldenSectionSearch.min eval : x x α h.SD * + eval : Δx h.SD : k 1 : k maxIters < h.SD x# F x Gradient - eval : h.SD 2^sqrt ε ≤ break β.PR h.SD transpose h.SD Δx - (* Δx transpose Δx * / eval : Δx h.SD β.PR Δx * + eval : α x α# h.SD * + F 010102 -^GoldenSectionSearch.min eval : x x α Δx * + eval : k k 1 + : 51 line if 21 line while x k 11 mat 21 mat 111 line :

α 10 :

x Rosenbrock 1 x 1 el - α sqrt x 2 el x 1 el (2^- (* 21 mat :

1121 mat Rosenbrock 0021 mat

x Rosenbrock 0.5 - 1.5 21 mat 0.001 50 NCGM.ref #

x Rosenbrock 0.5 - 1.5 21 mat 0.001 50100 NCGM 1.00014 1.00027 21 mat 1011 mat 21 mat

x Rosenbrock 0.5 - 1.5 21 mat 102 -^0.01 50100 NCGM.CD 0.99797 0.99584 21 mat 1411 mat 21 mat

x y Rosenbrock 1 x - α sqrt y x 2^- (* 21 sys :

11 Rosenbrock 0021 sys

x y Rosenbrock 0.5 - 1.5 21 mat 0.001 50100 NCGM 1.0001 1.0003 21 mat 1011 mat 21 mat

x y Rosenbrock 0.5 - 1.5 21 sys LevenbergMarquardt 1121 sys

x y Rosenbrock 0.5 - 1.5 21 mat 102 -^0.01 50100 NCGM.CD 0.99797 0.99584 21 mat 1411 mat 21 mat