First, please format your code so that it is readable by a human. Something like this
printf("No           root                   x[i+1]                 abs(x[i+1]-x[i])\n");
for i to n do
     y[i] := evalf(x[i]+(-D1(x[i])+sqrt(D1(x[i])^2-2*f(x[i])*D2(x[i])))/D2(x[i]));
     x[i+1] := evalf(y[i]-f(y[i])/sqrt(D1(x[i])^2-2*f(x[i])*D2(x[i])));
     printf("%d         %10.10f     %10.10f       %10.10e \n",
             i+1,       x[i+1],    f(x[i+1]), abs(x[i+1]-x[i])
     );
     if abs(x[i+1]-x[i]) < tol then
          print("approximate solution" = x[i+1]);
          print("No of iterations" = i+1);
          break
     end if
end do;

What is y[i]? What are D1 and D2? Did you intend for n to represent the maximum allowed number of iterations? n and tol and f need to be specified. Your formula for x[i+1] looks weird---too complicated. What function are trying to find the root of?

This is the kind of error message that a programmer puts into code to indicate that a serious bug has occured. This error message in particular occurs in the short procedure DynamicSystems:-TF_Matrix.

@jelmew I tested this on the uploaded worksheet:

evalindets(combine(Mcross, symbolic), sqrt, expand);

Maybe there are no solutions. It would be nice to have some evidence that a solution exists (such as a plot) before fine tuning fsolve with options.

There are complex solutions that fsolve will find if you give it the option complex.

@Adri van der Meer Regarding your point (1): It is not necessary to declare the dimensions of an Array. See my Answer for an example of this.

@Preben Alsholm These links cover the univariate case only.

@john125 Can you post a worksheet with the actual equations, please?

@john125 Sorry, I meant

select(y-> is(y>0), [Sols]);

@toandhsp Cut and pate Kitonum's code directly from the Post.

@acer Why are your exponents off by 4 decimal places compared to the OP's?

@toandhsp Did you get no result, or did you get a RootOf result? If the latter, add the explicit option to the command:

solve({30+1144*r^4-832*r^2=0, r>0}, explicit);

@ctnaz I know that *F means multiply by F, but you have "*F" not *F. What is the purpose of the quotation marks?

@Preben Alsholm

Saying the same thing differently, in a way that seems clearer to me: Reading the file with read is equivalent to executing b:= 2*z at the global level, regardless of where the read statement is placed.

I recall reading this in a help file, but I can't find it at ?read or ?parse. Preben, can you find it in help?

I also believe that reading a text file (as opposed to a .m file) with read is equivalent to applying parse to the file's contents, but I can't find this in help.

Indeed, MaplePrimes should have a rule that you need a certain level of reputation in order to Edit Questions after they have Answers!

@Markiyan Hirnyk It can't be a comment to your Answer because I wrote it before reading your Answer.