Some matrix factorization identities for discrete inverse scattering (Q1073130)

This paper shows that the triangular factorization of a given positive definite Toeplitz matrix lies at the heart of the traditional approaches for inverse problems. It is also shown that the various inversion methods implicitly obtain the factorization by solving different nested sets of linear equations and expressing the factors in terms of the solutions obtained. The factorization results obtained in this paper are somewhat more general than the ones used in Toeplitz assumption.