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On Singular Interval Systems Gtz Alefeld1 and Gnter Mayer2
 

Summary: On Singular Interval Systems
Götz Alefeld1 and Günter Mayer2
1 Universität KarIsruhe, 76128 Karlsruhe, Germany
goetz.alefeld@math.uni-karlsruhe.de
2 Universität Rostock, 18051 Rostock, Germany
guenter.mayer@mathematik.uni-rostock.de
Abstract. We consider the interval iteration [x]kH = [A][X]k+ [b]with
p(I[A]I) ::; 1 where I[A]I denotes the absolute value of the given interval
matrix [A]. If I[A]I is irreducible we derive a necessary and sufficient
criterion für the existence of the limit [x]*= [x]*([x]o)of each sequence
([xt) of interval iterates. In this way we generalize a well-known theorem
of O. Mayer [6] on the above-mentioned iteration, and we are able to
enclose solutions of certain singular systems (I - A)x = b with A E [A]
and degenerate interval vectors [b]==b. Moreover, we give a connection
between the convergence of ([X]k) and the convergence of the powers of
[A].
1 Introduction
Consider Poisson's equation
[Pu [Pu
ßS2 + ßt2 = - f(s, t) (1)

  

Source: Alefeld, Götz - Institut für Angewandte und Numerische Mathematik & Fakultät für Mathematik, Universität Karlsruhe

 

Collections: Mathematics