<DOC>
<DOCNO>
738
</DOCNO>
<TITLE>
finding zero's of arbitrary functions .
</TITLE>
<AUTHOR>
frank,w.l.
</AUTHOR>
<BIBLIO>
j. assoc. comput. mach. 5, 1958, 154.
</BIBLIO>
<TEXT>
  a method for finding real and complex
roots of polynomial equations, due to
d. muller, is applied to finding roots of
general equations of the form f(z) = 0,
where f(z) is analytic in the neighborhood
of the roots .  the procedure does not
depend on any prior knowledge of the
location of the roots nor on any special
starting process .  all that is required is
the ability to evaluate f(z) for any desired
value of z .  multiple roots can also be
obtained .  a general purpose program,
prepared for the univac scientific 1103
and 1103a, is described and numerical
results are presented for the following
applications ..  finding eigenvalues of differential
operators ,. finding eigenvalues of
arbitrary matrices ,. finding zeros of the
generalized eigenvalue problem ,. finding
roots of a number of transcendental
equations .
</TEXT>
</DOC>
