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Syntax |
levinson( r, b) |
See Also | toeplitz , tridiag , matrix division |
T x = b
for x
,
where T
is the Toeplitz matrix defined by
/ 1 if i = j
T = {
i,j \ r otherwise
|i - j|
The column vectors r and b
must be real or double-precision and have the same length.
The return value has the same number of rows as b
and is real, if both b and r are real and
double-precision otherwise.
/ 1 .5 \ / x \ / 1 \
| | | 1 | = | |
| | | | | |
\ .5 1 / \ x / \ 2 /
2
If you enter
r = {.5d0, .25}
b = {1.d0, 2.}
levinson(r, b)
O-Matrix will respond
{
0
2
}
which is the value of the vector x
that solves the equation above.
Note that the vectors r and b
must be of the same length even though the last component of
r is not used.