On Wednesday, June 10, 2015 at 5:53:16 PM UTC+2, Shivam Vats wrote: > > Mario, the algorithm looks quite similar to the Newton > method you have used for functional inverses for > expanding tan and tanh. We could also expand `sin/cos`. > Which one do think should be faster? > > Also, can the convergence of the method be proven? > I could not find any reference to it (except the algorithm > in Computer Arithmetic by Paul Zimmerman). >
Series reversion is a purely formal operation, so it always converges. For a faster algorithm to compute the reversion of a generic power series, see my paper http://fredrikj.net/math/reversion.html (a "generic" power series being given by a list of coefficients -- there are better methods for computing inverse series of functions composed from elementary functions like sin(sin(x))). Fredrik -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/c7431604-65bc-493b-b42b-91cd2073b392%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
