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Solving A Symmetric Toeplitz System Using Levinson's Algorithm

Description
Uses Levinson's algorithm to solve the equation 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.

Example
The following is a Toeplitz system of equations:
/ 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.