- #1
zetafunction
- 391
- 0
can a function in ONE dimension have NO inverse ?? i mean
if given the inverse function [tex] f^{-1} (x) = g(x) + \sum_{k=-N}^{k=N}c_{k}exp(ixlogk) [/tex]
the first function g(x) is an smooth function , the last Fourier series is a 'noise correction' t o this function g , N is a big but finite number (otherwise the OFurier series could diverge)
how could i use numerical methods to get f(x) ??
g(x) is always an INCREASING function.
if given the inverse function [tex] f^{-1} (x) = g(x) + \sum_{k=-N}^{k=N}c_{k}exp(ixlogk) [/tex]
the first function g(x) is an smooth function , the last Fourier series is a 'noise correction' t o this function g , N is a big but finite number (otherwise the OFurier series could diverge)
how could i use numerical methods to get f(x) ??
g(x) is always an INCREASING function.