Einladung zu einem Vortrag von:
Dr. Anton Iliev
University of Plovdiv
Dienstag, 18. März 2003,
15:30 Uhr, T 811
Iteration Methods for Simultaneous Extraction of a Part
of All Roots of Algebraic Equations
The problem of finding the roots of equations arises in solving
important theoretical and practical problems, such as
characteristic equations of matrices and differential or
difference equations. The numerous methods developed for solving
such equations fall into two basic categories: methods for
individual and simultaneous determination of the roots. Individual
roots can be found by various methods. Over the past several
decades, methods for simultaneous finding of all roots (SFAR) have
been developed. This fact is explained by two reasons: first,
these methods are more stable and have wider domains of
convergence; second, these methods are well suited for
implementation on computers with parallel processing.
Historically, it is interesting to note that Weierstrass predicted
such methods in 1891. Each method for SFAR admits a Gauss-Seidel
modification, which leads to better approximations at every step,
but rules out any possibility of parallel determination of the
roots. When such parallel method is implemented on a parallel
computer, the computations are shared between different
processors. The results obtained at each step are exchanged, and
the process of finding of roots is accelerated. The task in this
lecture is to show how it can build iteration methods with raised
speed of convergence and at the same time they give opportunities
for simultaneous searching of only one part of all roots (real,
complex, lying in given area, satisfying given conditions).
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