A new implementation of restarted Krylov subspace methods for evaluating f (A) b for a
function f, a matrix A and a vector b is proposed. In contrast to an implementation proposed …

For any linear system A x\approx b we define a set of core problems and show that the
orthogonal upper bidiagonalization of [b, A] gives such a core problem. In particular we …

Regularization techniques based on the Golub-Kahan iterative bidiagonalization belong
among popular approaches for solving large ill-posed problems. First, the original problem …

We describe how variable precision floating point arithmetic can be used in the iterative
solver GMRES. We show how the precision of the inner products carried out in the algorithm …

In this brief paper, we propose a time-domain data-driven method for model order reduction
by two-sided moment matching for linear systems. An algorithm that asymptotically …

This paper presents a multi-objective optimization approach for choosing an appropriate
regularization parameter in Tikhonov-type regularization of discrete ill-posed problems …

This paper revisits the analysis of the total least squares (TLS) problem AX≈ B with multiple
right-hand sides given by Van Huffel and Vandewalle in the monograph, The Total Least …

Minimum residual norm iterative methods for solving linear systems Ax= b can be viewed as,
and are often implemented as, sequences of least squares problems involving Krylov …

Under the Golub–Van Loan condition for the existence and uniqueness of the scaled total
least squares (STLS) solution, a first order perturbation estimate for the STLS solution and …

The standard approaches to solving an overdetermined linear system Ax≈ b find minimal
corrections to the vector b and/or the matrix A such that the corrected system is consistent …