Re: HELP!! (implied multiplication)

[Prev][Next][Index][Thread]

Re: HELP!! (implied multiplication)

My oh my. First it would be kind of nice to know to whom I am talking. Who is
"Doc" when he isn't hiding behind a handle?

I would appreciate it if you could dig around and find "10/2x" or something
similar in a paper or book of respectable lineage (published in a journal that
prints papers with mathematics). If you can, then I err, and will go off in a
corner and cry. If not, then do you think it wise to train students according
to
the operational precedence of one particular language or calculator? Won't they
run into trouble in the future?

As far as the numerical analysis, I have some credentials in this area, and
neither of the calculators uses the best algorithms. I haven't looked at the 89
(92), but I hope that they have done better this time.

Algorithms require study, and I think it would be a very unusual instructor who
would have the time or expertise to evaluate the ones in a calculator. It
really
isn't a trivial thing. TI and HP would do us a world of service if they cared
enough to ask a few numerical analysts to look over their algorithmic choices
so
that we could have confidence in their results.

Here is one  test you might care to use check out your calculator. The inverse
of the matrix A= (eI + 11') is (1/e)(I - 1 Inv(e+n) 1'), where e is a small
constant, I the nxn identity matrix, Inv() is the inverse operator,  and 1 is a
column vector of n unites (needless to say the prime denotes transposition).
Choose n=10, and e=0.000001, and ask your calculator to give you the inverse of
A. Compare it with the inverse given above and find the maximum error.

Householder or Givens or any other good algorithm will produce a max error of
about 0.00009 using double precision calculations. Excel gives 0.00007. the
HP48
gives 0.00055, and the TI85 gives 0.0032. There is no excuse for this. The code
required to use a better algorithm is both short and fast. I suspect that  the
algorithms in the calculators were taken from books published in the
pre-computer era.  The problem has practical importance, since real data
frequently has nearly linerally dependent columns.

--
Bob Wheeler --- (Reply to: bwheeler@echip.com)
        ECHIP, Inc.

Doc wrote:

> I completely disagree.  Neither evaluation of 10/2x is undefined, and thus
> to make it undefined simply because it is ambiguous is foolish.  I wonder
> how you would measure up to either TI or HP's numerical analysis staff?
> Think about what you're saying before you go criticizing others.
> You say that these devices should be an adjunct to teaching, and I
> completely agree with you.  There is, however, a certain amount of learning
> necessary before one can use almost ANY complex tool.  Modern
> graphing/programmable calculators are no exception to the case.  Your
> suggestion that instructors ought to be able to reference this type of
> equation without checking the specifics is like getting in a car and hitting
> the gas without checking to see if there is a brake or not.
>
> -Doc
>
> -----Original Message-----
> From: Bob Wheeler <bwheeler@ECHIP.COM>
>
> >Both TI and HP have made poor choices in this. Expressions such as 10/2x
> >should be undefined because it is ambiguous. Neither TI nor HP seem to have
> >had talented people in numerical analysis when they put their software
> >together, and hence this sort of problem occurs frequently, due in large
> part
> >to the desire of programers for a "friendly" calculator. It is a shame,
> since
> >both companies produce devices that should be an adjunct to teaching:
> >something that instructors ought to  able to reference in general without
> >having to check the
> >specifics themselves.  This is just the tip of the iceberg. When one gets
> into
> >the algorithms involved in integration, differential equations, linear
> >algebra, etc. the situation is bad indeed. There is no excuse for this,
> since
> >the calculators  have the capacity to do things both correctly and faster..
> >
> >--
> >Bob Wheeler --- (Reply to: bwheeler@echip.com)
> >        ECHIP, Inc.
References: