how to avoid numeric error

• To: mathgroup at smc.vnet.net
• Subject: [mg20309] how to avoid numeric error
• From: "Atul Sharma" <atulksharma at yahoo.com>
• Date: Fri, 15 Oct 1999 20:20:40 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```I am at a loss to explain this behavior, though I perhaps
misunderstand how Mathematica implements it's machine precision routines.
This is a simple example of a problem that cropped up during evaluation of
constants of integration
in a WKB approximation, where I would get quite different results depending
on how the constant was evaluated. I have localized the discrepancy to one
term of the form shown below:

testParameters =
{x1 -> 5.2, x2 -> 0.3, x3 -> 0.002, x4 -> -0.00025}

(-x1)^(-(x2 + x3)/x4) /. testParameters

In this case, as it turns out, x1 = -5.2, which is a floating point number,
and the exponent = 1208 (which may be integer or floating point, but is
floating point in this case).
I assumed that the result would be evaluated to machine precision in either
case,
since x1 is a float regardless. However, depending on whether the exponent
is integer or not, I get two different results, with a large imaginary
component

In[27]:=
(-5.2)^1208.

Out[27]=
8.55143720266536543174145`12.6535*^864 -
2.48026735232231456274073`12.6535*^852*I

In[28]:=(-5.2)^1208

Out[28]=
8.55143720266675767908621`12.8725*^864

I assume that this has some simple relationship to machine precision and
round-off error, but am I wrong in assuming that x1 should determine the
numeric precision of the entire operation?

I am using Mathematica 3.01.1 on a PC/Win95 platform.

I also encountered another problem, which bothers me because it's so
insidious. In moving a notebook from one machine to another by floppy (work
to home), a parsing error occurred buried deep inside about 30 pages of
code. A decimal number of the form 1.52356 was parsed as 1.5235 6 with a
space inserted and interpreted as multiplication. The same error occured in
the same place on several occasions (i.e. when I start getting bizarre
results, I know to go and correct this error).

I know these sound minor, but they have a large effect on the solution and
could easily go undetected. Thanks in advance.

A. Sharma

--------------------------------------------------
Atul Sharma MD, FRCP(C)
Pediatric Nephrologist,
McGill University/Montreal Children's Hospital

```

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