Complex Zeros of Functions

Complex zeros of a function of z=x+i*y are computed using graphics and Muller's method.

Interactive graphics and Muller's method
are used to compute function roots in a rectangular region of the complex plane. Function interact employs surface and contour plots of -log(abs(function(z))) to locate function roots which are read
interactively with the graphics cursor and then corrected by function muller which computes one or several roots at a time. Ten examples involving various special functions are presented.

The rootfinding function muller can be used separately to seek a number of real or complex roots starting with estimated values. Read the documentation in muller for details. For discussion of the search method and the example functions, appropriate references are:

Elementary Numerical Analysis' by S.D. Conte and Carl de Boor
and
'Handbook of Mathematical Functions' by Milton Abramowitz and Irene A. Stegun

The following functions and files are included:
interact.m - interactive driver program using graphics and function muller compute roots in a user chosen region of the complex plane
muller.m - a function based on Muller's method employing quadratic interpolation and deflation to compute
one or several roots of a general complex valued function
erfs.m - Error function of complex argument
gammac.m - Gamma function of complex argument
fresnels.m - Fresnel sine integral of complex argument
fresnelc.m - Fresnel cosine integral of complex argument
zetac.m - Riemann zeta function of complex argument
runexamples.m - a script file which analyzes ten examples dealing with various special functions
runexamples.doc - a listing of the printed output produced from runexamples
examples.mat - a file containing the numerical results produced from runexamples
The command readme describes the workspace.