I am trying to numerically find the root of a function that looks a bit like:
1/x - (SchurDecomposition[A[x]][])[], where
A is some matrix using the syntax
f[x_?NumericQ] = 1/x - (SchurDecomposition[A[x]][])[]
However when I monitor the values of x evaluated using the option
StepMonitor :> Print[x], the first value that appears is far away (e.g. 6) from my specified start point (i.e. 3). Does anybody understand why it is doing this? This is an issue since the value being used (in my example 6) lies far away from the attractor basin of the function and hence
FindRoot is giving me a wrong result. The initial starting value (in my example 3) lies very close to the root as I can see by plotting the function. In practice my numbers are a bit different and the function to calculate the matrix
A quite complicated, however these have been extensively verified and I am sure they are working correctly.
Thanks for your help.