I am currently having trouble inverting a complex matrix. I need to keep increasing the dimension of the matrix until the (1,1) term of the inverse of the matrix converges. I expect that I should only need to increase the dimension to ~10x10.
However as I increase the matrix size I get an error which says that the inverse of the matrix may contain significant errors due to the original matrix being badly conditioned. This could be due to some of the elements being very large (~10^20) when the matrix size is increased.
Is there a way around this? I have tried using the $MinPrecision command to set the precision to a really high number but this problem persists.
I don't need any other part of the inverted matrix except the (1,1) element so perhaps I do not need to compute the inverse of the full matrix?
I have attached a copy of my Mathematica notebook.
Help would be greatly appreciated.
Attachment: Sample code.nb, URL: ,