Toeplitz.Levinson Function

Solves a toeplitz system.

Pascal

procedure Levinson(R: TVec; A: TVec);

Parameters	Description
R	can be real or complex. N is equal to R.Length-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.

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.