On Convergence Rates of Root-Seeking Methods

[Namir]

Hi All,

I posted my study on convergence rates for root-seeking methods. Click here to download the ZIP file that contains the report, as a PDF file, and the macro-enabled Excel files that I used in the study.

My study looks at the effective convergence rate that manifests itself in the entire iteration process (from the initial guess to the refined root guess that meets the tolerance requirements) AND also the convergence rate calculated for each iteration. It seems that the theoretical convergence rate manifests itself ONLY FOR A FEW ITERATIONS .. which is very disappointing to me. I always thought that after the first few iterations, the root refinement process reaches a steady state which adheres to the theoretical convergence rate. This is NOT the case, unless the initial root guess is very very close to the root. I also discovered that using divided difference approximations for the derivatives slows down the convergence rate a bit.

Namir