Computation of a Class of COntinued Fraction Constants

There are numerous instances where mathematical constants do not admit a closed form. It is then of great interest to compute them, possibly in an efficient way. So the question is: does there exist an algorithm that computes the first d-digits of the constants and if so, what is the complexity in the number of arithmetic operations? We recall that a constant is said to be polynomial-time computable if its first d digits can be obtained with O(dr ) arithmetic operations. Here we consider a particular class of constants arising in the field of the dynamical analysis of algorithms and dynamical systems. The constants to compute are of a "spectral" nature since they are closely related to the spectrum of some transfer operators.

• Type: Conference
• Year: 2004
• Where: ALENEX
• Authors: Loïck Lhote
• Keywords: ALENEX 2004, ALENEX 2007, Arithmetic Operations, Mathematical Constants, Numerous Instances