How can I solve this?

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CHENG WEI LI
CHENG WEI LI 2022-10-23
回答： Torsten 2022-10-24
clc
clear
syms PL c k
eqn = [PL * exp(-c*exp(-k*0)) == 179323 ; PL * exp(-c*exp(-k*10)) == 203302 ; PL * exp(-c*exp(-k*20)) == 226542]
S = solve(eqn , [PL;c;k] )
S =
struct with fields:
PL: [0×1 sym]
c: [0×1 sym]
k: [0×1 sym]
  2 个评论
Muhammad Usman
Muhammad Usman 2022-10-23
the set of equations are non linear in nature that's why you can't use solve to compute the solution
Walter Roberson
Walter Roberson 2022-10-23
The equations have no solution over reals.

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回答（2 个）

Muhammad Usman
Muhammad Usman 2022-10-23
Ran in:
% Solve the system of equations starting at the point [0,0,0].
% PL = x(1); c = x(2); k = x(3);
% Initial guess is [0,0,0], you can change it accordingily
fun = @root2d;
x0 = [0,0,0];
x = fsolve(fun,x0)
Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm instead.
No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance, but the vector of function values is not near zero as measured by the value of the function tolerance.
x = 1×3
1.0e+05 * 2.0192 -0.0000 0
function F = root2d(x)
F(1) = x(1) * exp(-x(2)*exp(-x(3)*0)) - 179323;
F(2) = x(1) * exp(-x(2)*exp(-x(3)*10)) - 203302;
F(2) = x(1) * exp(-x(2)*exp(-x(3)*20)) - 226542;
end
  2 个评论
CHENG WEI LI
CHENG WEI LI 2022-10-23
The function has correct answer.
why this answer is wrong
Alex Sha
Alex Sha 2022-10-24
There are actually numerical solutions like below:
x1: 446505.431672107
x2: 0.912262916225993
x3: 0.0148006249649759

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Torsten
Torsten 2022-10-24
Ran in:
syms PL c k
eqn1 = PL * exp(-c*exp(-k*0)) == 179323;
eqn2 = PL * exp(-c*exp(-k*10)) == 203302;
eqn3 = PL * exp(-c*exp(-k*20)) == 226542;
sPL = solve([eqn1 eqn2],[c,k]);
Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.
PLsol = solve(subs(eqn3,[c,k],[sPL.c sPL.k]),PL);
sck = solve([subs(eqn1,PL,PLsol),subs(eqn2,PL,PLsol)],[c,k]);
csol = sck.c;
ksol = sck.k;
vpa(PLsol)
ans = 
446505.43167210849515476976968181
vpa(csol)
ans = 
0.91226291622599614437018856917074
vpa(ksol)
ans = 
0.014800624964975891465693800088887

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