Related papers: Augmented unprojected Krylov subspace methods
The resolvent Krylov subspace method builds approximations to operator functions $f(A)$ times a vector $v$. For the semigroup and related operator functions, this method is proved to possess the favorable property that the convergence is…
Saddle-point systems appear in many scientific and engineering applications. The systems can be sparse, symmetric or nonsymmetric, and possibly singular. In many of these applications, the number of constraints is relatively small compared…
This paper discusses model order reduction of large sparse second-order index-3 differential algebraic equations (DAEs) by applying Iterative Rational Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics, multibody…
Rational Krylov subspace (RKS) techniques are well-established and powerful tools for projection-based model reduction of time-invariant dynamic systems. For hyperbolic wavefield problems, such techniques perform well in configurations…
We propose and compare goal-oriented projection based model order reduction methods for the estimation of vector-valued functionals of the solution of parameter-dependent equations. The first projection method is a generalization of the…
We present a new algorithm, FRiM (FRactal Iterative Method), aiming at the reconstruction of the optical wavefront from measurements provided by a wavefront sensor. As our application is adaptive optics on extremely large telescopes, our…
This letter describes an incremental multimodal surface mapping methodology, which represents the environment as a continuous probabilistic model. This model enables high-resolution reconstruction while simultaneously compressing spatial…
In this paper a new restarting method for Krylov subspace matrix exponential evaluations is proposed. Since our restarting technique essentially employs the residual, some convergence results for the residual are given. We also discuss how…
This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…
This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…
In the previous studies, the high-order gas-kinetic schemes (HGKS) have achieved successes for unsteady flows on three-dimensional unstructured meshes. In this paper, to accelerate the rate of convergence for steady flows, the implicit…
Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace…
In this paper I describe a new optimal Krylov subspace solver for shifted unitary matrices called the Shifted Unitary Orthogonal Method (SUOM). This algorithm is used as a benchmark against any improvement like the two-grid algorithm. I use…
Pipelined Krylov subspace methods (also referred to as communication-hiding methods) have been proposed in the literature as a scalable alternative to classic Krylov subspace algorithms for iteratively computing the solution to a large…
This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and…
This work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov-)Galerkin…
We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a…
This paper describes a novel approach to solving unstructured search problems using a classical, signal-based emulation of a quantum computer. The classical nature of the representation allows one to perform subspace projections in addition…
Projected gradient methods are widely used for constrained optimization. A key application is for partial differential equations (PDEs), where the objective functional represents physical energy and the linear constraints enforce…
This article introduces randomized block Gram-Schmidt process (RBGS) for QR decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm and inherits its key characteristics such as being more efficient and having…