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Re: fsolve

From: Ted Harding
Subject: Re: fsolve
Date: Wed, 9 Aug 1995 07:15:04 +0200 (BST)

( Re Message From: John Utz )
> much context deleted...
>       but,
>       in reference to your remark about appreciating the manner in 
> which a numericla method would work, do u have a good "big picture" book 
> or two we should take a look at?
>  John Utz     address@hidden

Hi John,
Don't know about one which is all nice big pictures, but the best "general
reader" book I know is

     Numerical Methods for Scientists and Engineers

     by R W Hamming (McGraw-Hill, 1962, 1973)

which (as you might expect from the author's name) derives an amazing
amount of insight into all sorts of topics by taking a "signal-processing"
slant. For instance (regarding Simpson's Rule for Integration):

    " The significance of the trapezoid rule going down while Simpson's
    formula goes up requires some explanation. Simpson's formula increases
    the amplitude of the higher frequencies whereas the trapezoid tends to
    smother them. Although not enough is actually known about roundoff
    effects, we know that sudden jumps in a function due to roundoff tend
    to produce some high frequencies; hence Simpson's formula amplifies
    these whereas the trapezoid rule tends to smother them. "

However, you really have to browse widely in the book in order to put
together a systematic picture of any topic (like "Quadrature").

Another book which is also very good and oriented towards implementintg
methods in programming languages is

    Numerical Recipes [FORTRAN] / Numerical Recipes in C // in PASCAL

    W H Press, B P Flannery, S A Teukolsky & W T Vetterling
    (Cambridge University Press, 1986 onwards)

which is very well written and well organised on a topic-by-topic basis:
some pretty good explanations too, and loads of model programs; but for
real insight I still turn to Hamming!

Hope this helps, and best wishes.
Ted.                                    (address@hidden)

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