GKB-FP: An algorithm for large-scale discrete ill-posed problems The authors present a new algorithm for discrete ill-posed problems, which is called GKB-FP. This method exploits the Golub-Kahan bidiagonalization algorithm together with Tikhonov regularization in the generated Krylov subspace. The regularization parameter for the projected problem is chosen by the fixed-point method already presented by the first author. A detailed convergence analysis is provided. The paper is enriched by many numerical results on well-known problems so that the effectiveness of the method appears comparable with other methods already used, and even better.