d453ee08-0f5c-484c-9755-73d72091d335 269 4 5 decimal

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

Solving a determined system of Non-linear equations

vector of guesses X0 10020030010101016 mat transpose :

3 appVersion 0.98.6179 ≡ work sheet timing 8 min 21 line

AlgLib Solver for a system of nonlinear equations(Uni) sol k 1 β f rows range u k el β k el : for β Jac u f u Jacobian : StepMax 0 : ε 1014 -^: 12 mat u X0 StepMax ε β f β Jac al_nleqsolve : 41 line :

user scale factor m 0.001 :

NOTE: 1. 6179 takes a system of 'n' equalities = 'n' parameters. 2. 6671 supports n > parameters

Ua b β ia 2 β 3 el / 1 β 2 el / Ua * 1 β 2 el 1 β 1 el / β 6 el b + β 4 el Ua 2^+ sqrt / + (* exp + ln * (β 5 el^* :

Solver function β f 400 β ia 1.044 m * - 1200 β ia 2.679 m * - 2100 β ia 4.749 m * - 20 0.5 - β ia 0.18 m * - 120 0.5 - β ia 1.66 m * - 240 0.5 - β ia 4.3 m * - 61 mat :

CWD C:\SmathFile CurrentDirectory :

sol CWD nleq wfile 1

β CWD nleq rfile :

β f 3106 -^* 1105 -^* - 9106 -^* 9106 -^* - 1105 -^* 7106 -^* - 61 mat

Solver function x β plot x 0 β ia x 0.5 - β ia x 1 - β ia x 1.5 - β ia x 2 - β ia x 2.5 - β ia x 3 - β ia x 3.5 - β ia 81 mat :

x β plot 1 el x β plot 2 el x β plot 3 el x β plot 4 el x β plot 5 el x β plot 6 el x β plot 7 el x β plot 8 el 8 1 sys

β 581.3492 126.57 1014.7684 1263.2514 1.5268 0.7362 61 mat

6.4545 106 -^* - 4.2665 105 -^* - 4.8754 105 -^* 1.4972 105 -^* 3.4287 106 -^* - 2.1608 105 -^* - 8.2336 105 -^* - 3.3747 105 -^* 9.866 107 -^* - 3.1778 105 -^* - 5.7125 105 -^* 3.4146 105 -^* - 121 mat

x f x 040 ia 1.044 m * - x 0120 ia 2.679 m * - x 0210 ia 4.749 m * - x 0.5 - 20 ia 0.18 m * - x 0.5 - 120 ia 1.66 m * - x 0.5 - 240 ia 4.3 m * - x 1 - 40 ia 0.132 m * - x 1 - 150 ia 1.278 m * - x 1 - 270 ia 3.779 m * - x 1.5 - 60 ia 0.032 m * - x 1.5 - 180 ia 0.935 m * - x 1.5 - 300 ia 3.333 m * - 121 mat ≡

6671 solves this overdetermined system ... however, less accurate

100.8584 1038.0941 2037.1068 407.5965 1.5433 0.7167 61 mat

vector of guesses X0 5001007008002116 mat transpose :

ε 1015 -^:

581.3492 126.57 1014.7684 1263.2514 1.5268 0.7362 61 mat

s b x ia 2 s 3 el / 1 s 2 el / x * 1 s 2 el 1 s 1 el / s 6 el b + s 4 el x 2^+ sqrt / + (* exp + ln * (s 5 el^* :

s Φ s 040 ia 1.044 m * - s 0120 ia 2.679 m * - s 0210 ia 4.749 m * - s 0.5 - 20 ia 0.18 m * - s 0.5 - 120 ia 1.66 m * - s 0.5 - 240 ia 4.3 m * - 61 mat :

L s Φ X0 ε LevenbergMarquardt :

L 1112.4937 122.1498 973.5161 1332.718 1.543 0.7597 61 mat

x f 1 x exp + ln 1^:

0 f 0.6931

x f x x f x - x 1 - f x 2 - f x 3 - f 6 1 sys