Texas Instruments TI-89 Tip List page 174

The function parameters are
clist
fguess
yval
yemax
yetype
fipoly() returns the solution as a numeric value, if it can find one. If it cannot find a solution, it returns
the string "fipoly iterations". If you call fipoly() from another program, that program can use gettype() to
detect the error, like this:
fipoly(...)→x
if getype(x)≠"NUM" then
{handle error here}
endif
{otherwise proceed}
With fipoly(), you can specify the y-error yemax as either a relative or absolute error. If y
approximate value and y is the actual value, then
absolute error = y − y a
You will usually want to use the relative error, because this is the same as specifying the number of
significant digits. For example, if you specify a relative error of 0.0001, and the y-values are on the
order of 1000, then fipoly() will stop when the y-error is less than 0.1, giving you 4 significant digits in
the answer.
However, suppose you specify an absolute error of 1E-12, and the y-values are on the order of 1000
as above. In this case, fipoly() will try to find a solution to an accuracy in y of 1E-12, but the y-values
only have a resolution of 1E-10. fipoly() won't be able to do this, and will return the error message
instead of the answer.
As an example, I'll use the same gamma function approximation function from tip [11.5]. The function
to be solved is
y = a + bx + cx 2 + dx 3 + ex 4 + fx 5 + gx 6 + hx 7 + ix 8
where these coefficients are saved in a list variable called fclist:
a = 4.44240042385
d = -11.0699337662
g = 0.494033458314
Using curve fitting software for a PC, I found this estimating function:
x = p + qy + ry 2 + sy 3 + ty 4 + uy 5
where these coefficients are saved in a variable called fglist:
p = -788.977246657
List of coefficients for the polynomial that is to be solved.
List of coefficients of the estimating (guess) polynomial
The point at which to solve for x
The maximum desired y-error at the solution for x, must be >0
A string that specifies whether yemax is absolute error or relative error:
"abs" means absolute error
"rel" means relative error
b = -10.1483412133
e = 6.01503554007
h = -.0656632350273
q = 3506.8808748
y−y a
relative error =
y
c = 13.4835814713
f = -2.15531523837
i = 0.00388944540448
r = -6213.31596202
is the
a
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