The numerical stability of the lattice algorithm for least squares linear prediction problems

The numerical stability of the lattice algorithm for least-squares linear prediction problems is analysed. The lattice algorithm is an orthogonalization method for solving such problems and as such is in principle to be preferred to normal equations approaches. By performing a first-order analysis of the method and comparing the results with perturbation bounds available for least-squares problems, it is argued that the lattice algorithm is stable and in fact comparable in accuracy to other known stable but less efficient methods for least-squares problems.Dedicated to Germund Dahlquist on the occasion of his 60th birthday.This work was partially supported by NSF Grant MCS-8003364 and contracts AFOSR 82-0210, ARO DAAG29-82-K-0082.