void Levinson(TVec R, TVec A)
Solves a toeplitz system.
| # | Name | Description |
|---|---|---|
| 1 | A | The solution is stored in vector A. The first element of A at Index 0 is set to 1. The sign '*' stands for conjugation. |
| 2 | R | can be real or complex. N is equal to R.Length-1. |
Result: stored in self (calling object)
Remarks:
The procedures solves Toeplitz system of linear equations defined as:
[ R(0) R(1)* ... R(N-1)* ] [ A[1] ] = [ -R[1] ] [ R(1) R(0) ... R(N-2)* ] [ A[2] ] = [ -R[2] ] [ .... . . ] x [ . ] = [ . ] [ R(N-2) R(N-3) ... R(1)* ] [ A[N-1] ] = [ -R[N-1] ] [ R(N-1) R(N-2) ... R(0) ] [ A[N] ] = [ -R[N] ]
The computational complexity of the algorithm is O(n2) as oposed to at least O(n3) for LUSolve.
See Also: Toeplitz.ToeplitzSolve