In this paper we analyze the behavior of the LSQR algorithm for the solution of compact operator equations in Hilbert spaces. We present results concerning existence of Krylov solutions and the rate of convergence in terms of an ℓp sequence where p depends on the summability of the singular values of the operator. Under stronger regularity requirements we also consider the decay of the error. Finally we study the approximation of the dominant singular values of the operator attainable with the bidiagonal matrices generated by the Lanczos bidiagonalization and the arising low rank approximations. Some numerical experiments on classical test problems are presented.

10aCompact operator10aLanczos bidiagonalization10aLinear ill-posed problem10aLSQR1 aCaruso, Noe1 aNovati, Paolo uhttps://www.sciencedirect.com/science/article/pii/S0024379519303714