Function hilbert, Function hilbert ,10-14 – HP 50g Graphing Calculator User Manual
Page 315
Page 10-14
For example, the following command in ALG mode for the list {1,2,3,4}:
In RPN mode, enter
{1,2,3,4} ` V NDERMONDE.
Function HILBERT
Function HILBERT creates the Hilbert matrix corresponding to a dimension n. By
definition, the n
×n Hilbert matrix is H
n
= [h
jk
]
n
×n
, so that
The Hilbert matrix has application in numerical curve fitting by the method of
linear squares.
A program to build a matrix out of a number of lists
In this section we provide a couple of UserRPL programs to build a matrix out of
a number of lists of objects. The lists may represent columns of the matrix
(program
@CRMC) or rows of the matrix (program @CRMR). The programs are
entered with the calculator set to RPN mode, and the instructions for the
keystrokes are given for system flag 117 set to SOFT menus. This section is
intended for you to practice accessing programming functions in the calculator.
The programs are listed below showing, in the left-hand side, the keystrokes
necessary to enter the program steps, and, in the right-hand side, the characters
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
−
−
−
−
1
2
1
3
2
3
3
1
2
2
2
2
1
1
2
1
1
1
1
1
1
n
n
n
n
n
n
n
x
x
x
x
x
x
x
x
x
x
x
x
L
M
O
M
M
M
L
L
L
1
1
−
+
=
k
j
h
jk