A direct solver for solving systems of linear equations with banded ill-conditioned Toeplitz matrices

In this paper, the banded toeplitz matrices generated by are studied. the function is a real non-negative function with a zero of order at and the generated matrices are ill-conditioned hermitian positive definite. we show that these banded toeplitz matrices are similar to the banded real symmetric positive definite toeplitz matrices that are generated by . a fast direct solver is proposed to compute the inverse of these real matrices. numerical experiments show that our proposed method is faster and more stable than the stable levinson algorithm.