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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…
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…
For the solution of discrete ill-posed problems, in this paper a novel preconditioned iterative method based on the Arnoldi algorithm for matrix functions is presented. The method is also extended to work in connection with Tikhonov…
Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner-outer GMRES…
This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
Iterative algorithms are instrumental in modern numerical simulation for solving systems arising from the discretization of PDEs. They face however significant challenges in industrial applications, such as slow convergence, limit cycle…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems…
We present a modified version of the PRESB preconditioner for two-by-two block system of linear equations with the coefficient matrix $$\textbf{A}=\left(\begin{array}{cc} F & -G^* G & F \end{array}\right),$$ where $F\in\mathbb{C}^{n\times…
Well-conditioned spectral collocation and spectral methods have recently been proposed to solve differential equations. In this paper, we revisit the well-conditioned spectral collocation methods proposed in [T.~A. Driscoll, {\it J. Comput.…
In this work, we propose a reduced basis method for efficient solution of parametric linear systems. The coefficient matrix is assumed to be a linear matrix-valued function that is symmetric and positive definite for admissible values of…
Kernel methods are a popular class of nonlinear predictive models in machine learning. Scalable algorithms for learning kernel models need to be iterative in nature, but convergence can be slow due to poor conditioning. Spectral…
We discuss efficient solutions to systems of shifted linear systems arising in computations for oscillatory hydraulic tomography (OHT). The reconstruction of hydrogeological parameters such as hydraulic conductivity and specific storage…
We study the solution of large symmetric positive-definite linear systems in a matrix-free setting with a limited iteration budget. We focus on the preconditioned conjugate gradient (PCG) method with spectral preconditioning. Spectral…
In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
Constrained least squares problems arise in a variety of applications, and many iterative methods are already available to compute their solutions. This paper proposes a new efficient approach to solve nonnegative linear least squares…
High-quality reconstructions of signals and images with sharp edges are needed in a wide range of applications. To overcome the large dimensionality of the parameter space and the complexity of the regularization functional,…
Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…