HP 50g User Manual page 627

If p > n-1, then add columns n+1, ..., p-1, p+1, to V
In step 3 from this list, we have to be aware that column i (i= n+1, n+2, ...,
p+1) is the vector [x
rather than a vector, i.e., x = { x
i
sequence { x x
1
the COL menu to add those columns to the matrix V
After X is ready, and having the vector y available, the calculation of the
coefficient vector b is the same as in multiple linear fitting (the previous matrix
application). Thus, we can write a program to calculate the polynomial fitting
that can take advantage of the program already developed for multiple linear
fitting. We need to add to this program the steps 1 through 3 listed above.
The algorithm for the program, therefore, can be written as follows:
Enter vectors x and y, of the same dimension, as lists. (Note: since the
function VANDERMONDE uses a list as input, it is more convenient to enter the
(x,y) data as a list.) Also, enter the value of p.
Determine n = size of vector x.
Use the function VANDERMONDE to generate the Vandermonde
matrix V
If p = n-1, then
X = V
Else If p < n-1
Else
Convert y to vector
Calculate b using program MTREG (see example on multiple linear
fitting above)
Here is the translation of the algorithm to a program in User RPL language.
(See Chapter 21 for additional information on programming):
i i i
x ... x
1 2 n
i i
... x }. Then, we can transform this list into a vector and use
2 n
for the list x entered.
n
,
n
Remove columns p+2, ..., n from V
(Use a FOR loop and COL-)
Add columns n+1, ..., p+1 to V
(FOR loop, calculate x
]. If we were to use a list of data values for x
x ... x }, we can easily calculate the
1 2 n
i
, convert to vector, use COL+)
to form matrix X.
n
until X is completed.
n
to form X
n
to form X
n
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