相关论文: Inner Product Free Krylov Methods for Large-Scale …

We analyse the Krylov solvability of inverse linear problems on Hilbert space $\mathcal{H}$ where the underlying operator is compact and normal. Krylov solvability is an important feature of inverse linear problems that has profound…

The Stackelberg prediction game (SPG) is popular in characterizing strategic interactions between a learner and an attacker. As an important special case, the SPG with least squares loss (SPG-LS) has recently received much research…

We propose a matrix-free parallel two-level-deflation preconditioner combined with the Complex Shifted Laplacian preconditioner(CSLP) for the two-dimensional Helmholtz problems. The Helmholtz equation is widely studied in seismic…

The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…

For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by a white noise, the Lanczos bidiagonalization based LSQR method and its mathematically equivalent Conjugate Gradient (CG) method for…

In this work, we investigate various approaches that use learning from training data to solve inverse problems, following a bi-level learning approach. We consider a general framework for optimal inversion design, where training data can be…

This paper introduces and analyzes an original class of Krylov subspace methods that provide an efficient alternative to many well-known conjugate-gradient-like (CG-like) Krylov solvers for square nonsymmetric linear systems arising from…

In inverse problems we aim to reconstruct some underlying signal of interest from potentially corrupted and often ill-posed measurements. Classical optimization-based techniques proceed by optimizing a data consistency metric together with…

In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…

Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicability of these iterative methods in practice for…

The paper presents two variants of a Krylov-Simplex iterative method that combines Krylov and simplex iterations to minimize the residual $r = b-Ax$. The first method minimizes $\|r\|_\infty$, i.e. maximum of the absolute residuals. The…

We propose an inner product free iterative method called GP-CMRH for solving block two-by-two nonsymmetric linear systems. GP-CMRH relies on a new simultaneous Hessenberg process that reduces two rectangular matrices to upper Hessenberg…

Several Krylov-type procedures are introduced that generalize matrix Krylov methods for tensor computations. They are denoted minimal Krylov recursion, maximal Krylov recursion, contracted tensor product Krylov recursion. It is proved that…

In recent years two Krylov subspace methods have been proposed for solving skew symmetric linear systems, one based on the minimum residual condition, the other on the Galerkin condition. We give new, algorithm-independent proofs that in…

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…

In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well…

High frequency integral equation methodologies display the capability of reproducing single-scattering returns in frequency-independent computational times and employ a Neumann series formulation to handle multiple-scattering effects. This…

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…

In this work, we explore the application of multilinear algebra in reducing the order of multidimentional linear time-invariant (MLTI) systems. We use tensor Krylov subspace methods as key tools, which involve approximating the system…

We present a fundamentally new regularization method for the solution of the Fredholm integral equation of the first kind, in which we incorporate solutions corresponding to a range of Tikhonov regularizers into the end result. This method…