Convergence

[Guest]

I am trying to solve a nonlinear system in excel. Don't ask me why I'm not
using something faster. Does anyone know an easy way for vector-matrix
problems to converge to a solution for a large matrix computation problem?

 

[Niek Otten]

I think you'll have to provide some more details. What type of computation?
What is the role of the matrix? In your first post, you mention
Newton-Raphson. Why?
etc.

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Kind Regards,

Niek Otten

Microsoft MVP - Excel

 

[Guest]

f(X,P)= (sum(exp(g(x_i))^(1-s)/P_i))^(1/(1-s))

i=1,...,N
s>1 given
g is a linear function.
X, P are exogenous.
I have the coefficients and values of X and P, but I need to solve for
f(X,P), which is an N-vector.

I have a sheet that calculates each elemtent in sum(*) (there are N*N of
them) and a sheet (column) that calculates f(*) starting from an initial
value of, for example, 1, getting some new value. Using Newton-Raphson, I
have made a macro that calculates d(f_i(X_initial))/dx_j for all i=1, ... ,
Nl; j=1, ... N. This generates a matrix of gradients, which we then invert
to solve around the target value (the solution). I just wanted to see if
there was a way of doing this for a relatively large N (say 100) with less
steps.