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Good day every one

I have been trying to sove 3 non linear equations but i am "No solution found" report.

The code is as follows

I defined a function containing the 3 non linear equations in an mfile called "angle"

function F=myfunction(x)

F(1)=cos(-x(1)+x(2))+cos(-x(1)+x(3));

F(2)=cos(-x(2)+x(1))+cos(-x(2)+x(3));

F(3)=cos(-x(3)+x(1))+cos(-x(3)+x(2));

After running code

deltarad=fsolve(@yyyyy,rand([3 1]))

I get the following report

No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,

but the vector of function values is not near zero as measured by the

default value of the function tolerance.

<stopping criteria details>

deltarad =

-60.5208

-62.8602

-61.6905

fsolve stopped because the sum of squared function values, r, has gradient with

relative norm 7.341307e-07; this is less than options.OptimalityTolerance = 1.000000e-06.

However, r = 7.954251e-01, exceeds sqrt(options.FunctionTolerance) = 1.000000e-03.

Optimization Metric Options

norm(grad r) = 7.34e-07 OptimalityTolerance = 1e-06 (default)

r = 7.95e-01 sqrt(FunctionTolerance) = 1.0e-03 (default)

Matt J
on 21 Jan 2020

Edited: Matt J
on 21 Jan 2020

A numerical sweep also gives evidence that there is no solution

[x1,x2,x3]=ndgrid(linspace(-pi,+pi,512));

F1=cos(-x1+x2)+cos(-x1+x3);

F2=cos(-x2+x1)+cos(-x2+x3);

F3=cos(-x3+x1)+cos(-x3+x2);

F=[abs(F1(:)), abs(F2(:)), abs(F3(:))];

Fmin = min(sum(F,2))

Fmin =

1.0142

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Alex Sha
on 28 Jan 2020 at 15:43

Edited: Alex Sha
on 28 Jan 2020 at 15:44

Hi, all, how about the solutions below, from the numerical perspective：

1：

x1: -5.21219473201765E21

x2: -0.279500437676178

x3: 1.29129588911872

Fevl:

f1=0

f2=-1.4930819167841E-15

f3=-1.4930819167841E-15

2:

x1: -1.79664678356017E21

x2: 2.02595283616513

x3: 3.59674916296003

Fevl:

f1=0

f2=-3.04739415125932E-15

f3=-3.04739415125932E-15

3:

x1: 2.19768008763813

x2: 5.41140930100612E22

x3: 0.626883760843237

Fevl:

f1=3.61394399649162E-15

f2=0

f3=3.61394399649162E-15

Matt J
on 28 Jan 2020 at 15:51

I can't reproduce your f values

x1= -5.21219473201765E21

x2= -0.279500437676178

x3= 1.29129588911872

F1=cos(-x1+x2)+cos(-x1+x3)

F2=cos(-x2+x1)+cos(-x2+x3)

F3=cos(-x3+x1)+cos(-x3+x2)

F1 =

-0.2352

F2 =

-0.1176

F3 =

-0.1176

Walter Roberson
on 28 Jan 2020 at 17:10

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