01277nas a2200193 4500008004100000022001400041245006400055210006400119300001200183490000800195520068500203653002100888653003000909653002900939653000900968100001600977700001800993856007201011 2019 eng d a0024-379500aConvergence analysis of LSQR for compact operator equations0 aConvergence analysis of LSQR for compact operator equations a146-1640 v5833 a
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