Re: [Boost-users] TOMS748 question

On Thu, Jan 28, 2021 at 10:11 PM Shriramana Sharma wrote:

On Thu, Jan 28, 2021 at 5:57 PM Shriramana Sharma wrote:

...

https://github.com/boostorg/math/blob/develop/include/boost/math/tools/toms7...

Can you elucidate which step from the original paper this quadratic step corresponds to?

On more careful examination I see that 4.1.3 and 4.2.3 of the original paper have a n == 2 option, which would lead to a compulsory quadratic evaluation.

But still as per the paper, the step after such a compulsory quadratic step would branch into a quadratic_interpolate with count = 3, but in this implementation such a step is missed. I have no idea whether this will lead to inaccuracy, since further steps would definitely refine the bracket, but just placing this on record here. I was also thrown a bit by the redefinition of max_iter as “The maximum number of function invocations to perform in the search for the root”. To my understanding an iteration is defined by the loop in the algorithm, and the paper speaks of “3 or 4 function evaluations per iteration”. I realize I'm quibbling at semantics, and one may be free to either limit the number of iterations or function calls (mostly the former is done I think) but it may be better to rename the variable to max_funcalls or such to clarify its purpose and highlight the deviation from the original paper. Thanks, and please do respond when you can. -- Shriramana Sharma ஶ்ரீரமணஶர்மா श्रीरमणशर्मा 𑀰𑁆𑀭𑀻𑀭𑀫𑀡𑀰𑀭𑁆𑀫𑀸