Preconditioning strategies for asymptotically ill-conditioned block Toeplitz systems (Q1347078)

Linear systems with block Toeplitz matrices, of the kind one gets from a Fourier expansion of a continuous kernel over a square region, are solved with a preconditioned iteration, with a band block Toeplitz matrix as preconditioner. It is shown that the condition number of the preconditioned iteration can be bounded by a number independent of the block size and number of blocks.