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
