@dharr 

Thanks for confirming this .. I'll continue exploring this problem using the routines you provided.

Thank you for this - it is most helpful and I have learned a lot in the process. 

Yes .. I should have stated that both a and b are non-integers. 

Do you think that it is possible to extract a general expression for the roots of f (or g) in terms of a and b?

In the meantime, I will use your model to explore the (real) numerical solutions.

Interesting ...  it seems that your adjustment has resolved the problem .. thank you!

I didn't think about the followup process -  your advice is appreciated.

Thanks for the timely response.

As regards the expected values ...

Parameter a will typically take the value 0.1 and the index, m, will vary from 0.1 to 10

I'll take a look at the commands you suggested - so that will be helpful.

I appreciate your help!

@Carl Love 

Thanks so much for taking an interest in this and for providing me exactly what I need!

@jganding 

That's exactly what I was looking for!

Thanks for the quick response and the advice - especially on the use of the printf command.

I'm very grateful ..

@mmcdara 

I agree. Following your response, I reviewed the references you recommended and they are very interesting indeed.

Once again .. thanks for your help.

@mmcdara 

I thank you for taking the time to resolve this and to introduce me to the resources.

Your procedure will give me a good start! 

Thanks again!

@Christopher2222 

I appreciate this advice ... I'll give it a shot when I return to terra firma.

Thanks again!

@tomleslie 

This is exactly what I was looking for.

Many thanks to you for sharing this and for the speedy response.

Thanks for the link ... I'm sure that will do the trick!

@acer 

Hi - thanks for the quick response.

Here is the file (retrieved it from the old laptop).

Cluster_Analysis_Sep_23.mw

@Carl Love 

Thanks ... I'll do that.

@Carl Love 

I guess we'll wait and see. Thanks for persevering with this.

@Carl Love 

Hi again. 

The solution you provided is great .. thanks again.

Just a minor observation - if you don't mind me sharing. 

When I copy and paste your routines into my worksheet, the left-side labels of the dataframe equation does not appear on my screen (i.e. AtoB, BtoC, AtoC is absent). In other words, the three matrices are returned alone. However, I accidentally discovered that, when I undo the previous operation, the labels then appear!

I also noticed that when I execute your entire worksheet, it's fine!

Have you ever encountered this?