07/02/2014, 09:00 PM

An important concept is that the equations MUST also hold for :

sexp* ' (z)

This augments the number of equations.

If I am not mistaken by considering sexp* alone you get about N/sqrt(2) equations where N is the number of estimates on the bottom line.

by adding the requirement for the derivative you double the amount of equations so you get about sqrt(2) N equations.

The degree of the estimated truncated Taylor then has a degree somewhere between N / sqrt(2) - C and N sqrt(2) + C2 where the C's are constants.

This makes the idea more serious.

How to make the set of equations converging is another matter but it seems some kind of solvability , existance and uniqueness should be possible.

---

Btw convergance issues for systems of equations reminds me of an idea I had that my friend mick posted on MSE :

http://math.stackexchange.com/questions/...-growing-n

For those who are intrested.

Not sure if it helps here unless someone has a very general theory about convergance for systems of equations.

---

regards

tommy1729

sexp* ' (z)

This augments the number of equations.

If I am not mistaken by considering sexp* alone you get about N/sqrt(2) equations where N is the number of estimates on the bottom line.

by adding the requirement for the derivative you double the amount of equations so you get about sqrt(2) N equations.

The degree of the estimated truncated Taylor then has a degree somewhere between N / sqrt(2) - C and N sqrt(2) + C2 where the C's are constants.

This makes the idea more serious.

How to make the set of equations converging is another matter but it seems some kind of solvability , existance and uniqueness should be possible.

---

Btw convergance issues for systems of equations reminds me of an idea I had that my friend mick posted on MSE :

http://math.stackexchange.com/questions/...-growing-n

For those who are intrested.

Not sure if it helps here unless someone has a very general theory about convergance for systems of equations.

---

regards

tommy1729