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Tommy's matrix method for superlogarithm. - Printable Version

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Tommy's matrix method for superlogarithm. - tommy1729 - 05/07/2016

Essentially my matrix method is based on solving

F(x) = F(exp(x)) - 1

In terms of Taylor series.

We pick the expansion point x = 0 because the distance
Between the curve exp and id is minimum at x=0.

This is mentioned before here


http://math.eretrandre.org/tetrationforum/showthread.php?tid=3

The way I solve the infinite matrix is different.

First i solve the truncated linear with 7 variables and 6 equations.
And then minimize the Sum of squares for them.

Now i plug in the value of these 7 variables into the truncation 16 variables and 8 equations and again minimize the Sum of squares.

Then continue 34 equations and 17 variables etc etc.

By minimizing the Sum of squares we get the highest possible radius ( Up to the fixpoint ).

Since that radius extends to 1 we are Done.

Regards

Tommy1729