Numerics of analytic functions and complexity. (Numerik analytischer Funktionen und Komplexität.) (German) Zbl 0797.68090

Complexity in this survey means the number of bit-operations if all computations are performed numerically with binary numbers. Upper bounds are presented for various problems concerning specific analytic functions, such as: multiplication, division, multiple evaluation, and interpolation of polynomials and rational functions; composition and inversion of power series; factorization of complex polynomials into linear factors; determining the partial fraction representation of rational functions; determining power series representations of algebraic functions given implicitly by polynomial equations; evaluation of elementary functions such as exp, ln, sin, tan, etc., and evaluation of the \(\zeta\)-function.


68W30 Symbolic computation and algebraic computation
68Q25 Analysis of algorithms and problem complexity
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
11Y35 Analytic computations