Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Beitrge zur Numerischen Mathematik 12 (1984), 7-19
 

Summary: Beiträge zur Numerischen Mathematik
12 (1984), 7-19
On improving approximate triangular factorizations
iteratively
GÖTZALEFELD and JON G. ROKNE
Summary. Newton's methoq. applied iteratively to the improvement of an approximate
triangular factorization of a matrix is discussed in detail. Particular consideration is given to
the effect of rounding errors on the convergence of the iteration. It is shown that on a computer
employing fixed length floating-point arithmetic Newton's method converges with an arbi-
trary starti:m.g value after 2n-l steps to the same value as that obtained by Gaussian elimi-
nation. Finally, a new method is proposed for the iterative improvement of bounds for the
elements of the triangular factorization where the effects of the rounding errors are also
considered.
1. Intr:oduction
It is frequently necessary to solve a system of linear equations Ax = b for a variety
of right-hand sides b. Since this is often done by factoring A as (1 + L*) U* and
then solving the resulting simpler sets of equations, it is important to calculate L*
and U* as accurately as possible.
\Vith this in mind J. W. SCHMIDT[3] recently proposed to apply Newton's method
in order to correct an approximate factorization of a non-singular matrix A. SCH:MIDT

  

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

 

Collections: Mathematics