<p>Levenberg-Marquardt algorithm</p>

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Решение систем нелинейных уравнений методом Ньютона

Penyelesaian sistem persamaan nonlinear menggunakan metode Newton

in the collapsible area is an implementation of the Levenberg-Marquardt algorithm for nonlinear equation systems.

<p>Levenberg-Marquardt algorithm</p>

Levenberg-Marquardt algorithm x f x.0 ε LM k.max 100 : k 0 : ν 2 : p x.0 : τ 0.001 : n p f rows : m x.0 rows : ε.1 ε : ε.2 ε : ε.3 ε : ε.p y.0 p f - : j 1 n range k 1 m range J j k el p f j el p k el diff : for for A J transpose J * : I A rows identity : μ τ A Diag max * : stop J transpose p f * normi ε.1 ≤ : y.0 n Zeros : stop ¬ (k k.max < (& k k 1 + : Δp A μ I * + invert J transpose * p f * - : Δp norme ε.2 p norme * ≤ break p.new p Δp + : ρ ε.p norme (2^p f p.new f - norme (2^- (Δp transpose μ Δp * J transpose p f * + (* det / : ρ 0 > p p.new : ε.p p.new f p f - : j 1 n range k 1 m range J j k el p f j el p k el diff : for for A J transpose J * : I A rows identity : stop J transpose p f * normi ε.1 ≤ (: (ε.p norme (2^ε.3 ≤ (| μ μ 13 / 12 ρ * 1 - (3^- Max * : ν 2 : 81 line μ μ ν * : ν 2 ν * : 21 line if 31 line if 21 line 21 line while p k 21 mat 191 line :

Входные данные:

Data masukan:

input LM algorithm data:

Approximation x.0 11031 mat :

Equations set 1 x f 2 x 1 el * x 2 el + 2 x 3 el 2^* + 5 - x 2 el 3^4 x 3 el * + 4 - x 1 el x 2 el * x 3 el + e x 3 el^- 31 mat :

Accuracy ε 1015 -^:

Solution sol x f x.0 ε LM : 1.422 0.975 0.768 31 mat 1121 mat

x vector x sol 1 el : 1.422 0.975 0.768 31 mat

Number of iterations iter sol 2 el : 11

Входные данные:

Data masukan:

input data for the SMath - Levenberg-Marquardt algorithm

Equations set f 2 x 1 el * x 2 el + 2 x 3 el (2^* + 5 ≡ x 2 el (3^4 x 3 el * + 4 ≡ x 1 el x 2 el * x 3 el + e x 3 el^≡ 31 mat :

set of initial variables x.0 11031 mat :

f x.0 ε LevenbergMarquardt #

Erorr ε 1015 -^: