Iterative regularization and MINRES

M Kilmer, GW Stewart - SIAM journal on matrix analysis and applications, 2000 - SIAM
regularizing properties of MINRES. While our theory does not completely characterize the
regularizing … will be concerned with regularization based on the iterative method MINRES [9]. …

Iterative regularization with minimum-residual methods

TK Jensen, PC Hansen - BIT Numerical Mathematics, 2007 - Springer
iterative regularization, and in particular the minimum-residual methods GMRES and
MINRES, for which the projection onto the underlying Krylov subspace may have a regularizing ef…

On regularizing effects of MINRES and MR-II for large scale symmetric discrete ill-posed problems

Y Huang, Z Jia - Journal of Computational and Applied Mathematics, 2017 - Elsevier
… posed problems, MINRES and MR-II are often used iterative regularization solvers. We call
a regularized solution best possible if it is at least as accurate as the best regularized solution …

Smoothing-norm preconditioning for regularizing minimum-residual methods

PC Hansen, TK Jensen - SIAM journal on matrix analysis and applications, 2007 - SIAM
… the MINRES algorithm [14], the latter yielding a simpler implementation with a short recursion.
Regularizing GMRES and MINRES iterations … of regularizing iterations, we apply CGLS to …

[PDF][PDF] Three Results on Iterative Regularization

M Kilmer, GW Stewart - Institute for Advanced Computer Studies TR, 1998 - Citeseer
regularizing properties of MINRES. While our theory does not completely characterize the
regularizing … will be concerned with regularization based on the iterative method MINRES 8]. …

Accurate solution of weighted least squares by iterative methods

EY Bobrovnikova, SA Vavasis - SIAM Journal on Matrix Analysis and …, 2001 - SIAM
… This article presents an iterative algorithm for WLS problems called MINRES-L. The … systems
with iterative methods is called “regularization.” A typical regularization technique modifies …

Analysis of the minimal residual method applied to ill posed optimality systems

BF Nielsen, KA Mardal - SIAM Journal on Scientific Computing, 2013 - SIAM
… number of iterations required by the minimal residual (MINRES) … This suggests that the
MINRES scheme might not be well … iterative schemes can handle cases with small regularization

Obtaining Pseudo-inverse Solutions With MINRES

Y Liu, A Milzarek, F Roosta - arXiv preprint arXiv:2309.17096, 2023 - arxiv.org
… In Proposition 1, we relate the lifting strategy at iteration t of MINRES to the orthogonal
projection of the iterate xt onto AKt(A, b). Consequently, performing lifting at the final …

[PDF][PDF] Iterative methods for singular linear equations and least-squares problems

SC Choi - 2006 - academia.edu
MINRES-QLP appears to have a better regularization property than … We review the
iterative algorithms CG, SYMMLQ, and MINRES for Hermitian linear systems and least-squares …

Minres: From negative curvature detection to monotonicity properties

Y Liu, F Roosta - SIAM Journal on Optimization, 2022 - SIAM
… within a MINRES iteration holds the residual of the previous iteration is one such direction. …
Following [28], we consider a binary classification problem using a (regularized) nonlinear …