Levinson Routine

Summary

Solves a toeplitz system.

Declaration

Procedure Levinson(R, A: TVec);

Description

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. The solution is stored in vector A. The first element of A at Index 0 is set to 1. The sign " * " stands for conjugation. R can be real or complex. N is equal to R.Length-1;

See Also
ToeplitzSolve