R.W. Hamming on RoundOff


25 Sep 04 
Sven C. Koehler has started to read "Numerical Methods for Scientists
and Engineers". He was so kind to send me a few quotes he likes from
the introduction.
Most books on computing stress the estimation of roundoff,
especially the bounding of roundoff, but we shall concentrate
on the avoidance of roundoff. It seems better to avoid roundoff
than to estimate what did not have to occur if common sense and
few simple rules had been followed before the problem was put on
the machine.
Another standard algorithmic problem both in mathematics and in the use
of computation to solve problems is the solution of simultaneous linear
equations. Unfortunately much of what is commonly taught is usually not
relevant to the problem as it occurs in practice; nor is any completely
statisfactory method of solution known at present. Because the solution
of simultaneous linear equations is so often a standard library package
supplied by the computing center and because the corresponding
description is so often misleading, it is necessary to discuss the
limitations (and often the plain foolishness) of the method used by the
package. Thus it is necessary to examine carefully the obvious flaws and
limitations, rather than pretending they do not exist.
update: (sorry, German only;) A big thanks to Sven C. Koehler for this
summary
Ich habe es nun in den groessten Teilen ueberflogen. Die Ideen sind nicht
wirklich neu: Umformen von Gleichungen, Vermeiden ungefaehr gleichgrosse
Zahlen von einander abzuziehen, Approximation. Beim Loesen von
Gleichungssystemen schlägt er z.B. vor, ein Verfahren einzusetzen, das
kein wiederholtes Dividieren benoetigt, dann wird's auch nicht ungenau.
Trotzdem mag ich das Buch, weil es in mir den Eindruck weckt, dass es
sehr fundiert ist. Es ist voll von mathematischen Formeln, die ich alle
nicht wirklich verstanden habe, aber ich werde in jedem Fall wieder darin
nach Erklaerungen suchen, wenn ich mal wieder ein NumerikProblem habe.
Ich glaube für dich ist as Buch eher langweilig, das meiste kennst du
bestimmt aus dem Studium. :)
