A Continuum Limit of Matrix Inverse Problems
Percy A. Deift, Eugene Trubowitz · SIAM Journal on Mathematical Analysis · 1981
In this paper the authors consider the Lanczos algorithm for periodic Jacobi-matrix inverse problems. In the usual form this algorithm does not have a continuum limit, but by mixing periodic and antiperiodic spectra and introducing a set of weights, the authors show that the modified Lanczos scheme does indeed have a continuum limit. Moreover, this limit is precisely the inverse scheme for the Schrödinger equation which was introduced by the authors in [Comm. Pure Appl. Math., 32 (1979), pp. 121–151].