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HP HP-15C Advanced Functions Handbook

HP HP-15C
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Appendix: Accuracy
of
Numerical Calculations
203
and
50,000
50,000
p q
0
0.00002 50,000.03 48,076.98077...
0
0
50,000 48,076.95192...
00
0
0.00001923076923...
Ideally,
p = q = 0, but the
HP-lSC's
approximation
to X
1,
namely
(T/x](X),
has q =
9,643.269231 instead,
a
relative error
=
0.0964...,
llx-1!
nearly
10
percent.
On the
other hand,
if X + AX
differs
from
X
only
in its
second column where -50,000
and
50,000
are
replaced
respectively
by
-50,000.000002
and
49,999.999998 (altered
in the
llth
significant digit), then
(X +
AX)"1
differs
significantly
from
X'1
only insofar
as p 0 and q = 0
must
be
replaced
by p
=
10,000.00600...
and q =
9,615.396154....
Hence,
=
0.196...;
the
relative error
in (X + AX)
1
is
nearly twice
that
in
11/x|(X).
Do
not
try to
calculate
(X +
AX)"1
directly,
but use
instead
the
formula
(X
-
cb7)-1
=
X-1
+
X-WX-1
/
(1
-
b^X^c),
which
is
valid
for any
column vector
c and row
vector
bT,
and
specifically
for
andbr
= [0
0.000002
0 0] .
Despite
that
it can be
shown
that
no
very small end-figure perturbation
<5X
exists
for
which
(X +
5X)'1
matches
1
1/x|(X)
to
more
than
five
significant
digits
in
norm.

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HP HP-15C Specifications

General IconGeneral
BrandHP
ModelHP-15C
CategoryCalculator
LanguageEnglish

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