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Solving A Symmetric Toeplitz System Using Levinson's Algorithm
Syntax levinson(r, b)
See Also toeplitz , tridiag , matrix division

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.