Instability in the solution of banded Toeplitz systems
Allan J. MacLeod · IEEE Transactions on Acoustics Speech and Signal Processing · 1989
The author considers some algorithms for the solution of banded Toeplitz systems and calculates certain elements of the solution first and then the remaining elements by forward or backward substitution. It is shown that for symmetric matrices this method is almost always highly unstable. A numerical example is given to support the argument.>