Code covered by the BSD License
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[Zeros,Fzeros]=muller(fn,npre...
[Zeros,Fzeros]=muller(fn,nprev,maxit,ep1,ep2,fnreal,Zeros)
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[rts,frts,rtsm,frtsm,func]=in...
[rts,frts,rtsm,frtsm,func]=interact(func,xlim,ylim)
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f=zetac(x)
f=zetac(x) computes the Riemann zeta function
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v=erfs(z,N)
v=erfs(z,N) evaluates the series expansion for the
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v=fresnelc(z,N)
v=fresnelc(z,N) sums the Bessel series expansion of
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v=fresnels(z,N)
v=fresnels(z,N) sums the Bessel series expansion of
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v=gammac(z)
v=gammac(z) gives the gamma function for complex argument.
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readme.m
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runexamples.m
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View all files
complexzeros
by Howard Wilson
30 Aug 2009
Complex zeros of a function of z=x+i*y are computed using graphics and Muller's method.
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| File Information |
| Description |
This workspace employs interactive graphics and Muller's method
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 principal references for this work 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 to 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
fresenlc.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
examplesout.txt - a listing of the printed output produced
from runexamples
examples.mat - a file containing the numerical results
produced from runexamples
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| MATLAB release |
MATLAB 7.5 (R2007b)
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