On the block Lanczos and block Golub–Kahan reduction methods applied to discrete ill?posed problems

The reduction of a large-scale symmetric linear discrete ill-posed problem with multiple right-hand sides to smaller block tridiagonal matrix can easily be carried out by the application small number steps Lanczos method. We show that subdiagonal blocks reduced converge zero fairly rapidly increasing number. This quick convergence indicates there is little advantage in expressing solutions problems terms eigenvectors coefficient when compared using basis vectors, which are simpler and cheaper compute. Similarly, for nonsymmetric sides, we solution subspace defined few Golub–Kahan bidiagonalization method usually applied instead determined singular value decomposition without significant, if any, quality computed solution.