Hp 49g+ User Manual download pdf (Page 626)

100

101

Page 18-59

If p = n-1, X = V

If p < n-1, then remove columns p+2, …, n-1, n from V

to form X.

If p > n-1, then add columns n+1, …, p-1, p+1, to V

to form matrix X.

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

… x

]. If we were to use a list of data values for x

rather than a vector, i.e., x = { x

… x

}, we can easily calculate the

sequence { x

… x

}. Then, we can transform this list into a vector and

use the COL menu to add those columns to the matrix V

until X is completed.

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

for the list x entered.

• If p = n-1, then

X = V

Else If p < n-1

Remove columns p+2, …, n from V

to form X

(Use a FOR loop and COL-)

Else

Add columns n+1, …, p+1 to V

to form X

(FOR loop, calculate x

, convert to vector, use COL+)

• Convert y to vector

• Calculate b using program MTREG (see example on multiple linear

fitting above)

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Hp 49g+ User Manual Page 626

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