My professor is using the following slides:
What is epsilon algebra and why is it important in Numerical Analysis?
[Math] epsilon algebra and why is it important in Numerical Analysis
numerical methods
numerical methods
My professor is using the following slides:
What is epsilon algebra and why is it important in Numerical Analysis?
Best Answer
This is a question you should ask your professor. If they have not made it clear, then many students in the class are probably wondering about that.
The different epsilons represent small errors. That "epsilon algebra" is nothing but first order approximation of errors. All terms including products of epsilons is considered small and is thrown away. All that is left is the main term without any epsilons and terms linear in the epsilons.
When errors are small, such calculations give a decent approximation of propagation of errors. Errors are inevitable in numerical analysis, and it is important to understand how big an error you make in a calculation if you start with a given error. There are a number of sources of error, so it is convenient to have several epsilons.