Abstract. Some of the main results concerning Toeplitz matrix
computations are recalled, in particular the recent techniques of
the authors for the solution of banded Toeplitz systems are revisited.
These tools are used for the design and analysis of new algorithms
for solving block banded block Toeplitz systems with blocks that are banded
Toeplitz matrices, and for solving certain block tridiagonal block Toeplitz
systems with blocks having a tensor product structure.
Applications to queueing theory, polynomial computations and image
restoration are shown.
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