08/18/2016, 12:29 PM

I told this before but ...

Lets consider the system of equations from the OP.

We need to find v_n.

INSTEAD of truncating to n x n systems and letting n grow , i consider it differently.

We want the radius to be as large as possible.

So we minimize v_0 ^2 + v_1 ^2 + ...

And expect a radius Up to the fixpoints of exp.

We truncate to an n x (n+1) system and min the Sum of squares above for the relevant v_k.

So we take 9 equations with (v_1 ... v_10) and solve for the min of v_1 ^2 + ... v_10.

Then we proceed by adding 11 variables ( v_11,... v_22 ) and solve that system with plug-in the pevious values v_j and 10 equations , and again minimizing the Sum of squares.

Then repeat ...

So

V_1 .. V_10 then v_11 .. V_21 , v_22 ... V_33 etc

So eventually all v_j get solved.

And the equations hold almost at a triangulair number distance of iterztions.

Regards

Tommy1729

Lets consider the system of equations from the OP.

We need to find v_n.

INSTEAD of truncating to n x n systems and letting n grow , i consider it differently.

We want the radius to be as large as possible.

So we minimize v_0 ^2 + v_1 ^2 + ...

And expect a radius Up to the fixpoints of exp.

We truncate to an n x (n+1) system and min the Sum of squares above for the relevant v_k.

So we take 9 equations with (v_1 ... v_10) and solve for the min of v_1 ^2 + ... v_10.

Then we proceed by adding 11 variables ( v_11,... v_22 ) and solve that system with plug-in the pevious values v_j and 10 equations , and again minimizing the Sum of squares.

Then repeat ...

So

V_1 .. V_10 then v_11 .. V_21 , v_22 ... V_33 etc

So eventually all v_j get solved.

And the equations hold almost at a triangulair number distance of iterztions.

Regards

Tommy1729