Results 41 to 50 of about 78,319 (219)
Krylov subspace split Bregman methods [PDF]
, 2023 Split Bregman methods are popular iterative methods for the solution of large-scale minimization problems that arise in image restoration and basis pursuit. This paper investigates the possibility of projecting large-scale problems into a Krylov subspace
Alotaibi, Majed +2 more
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Krylov subspace methods for the Dirac equation [PDF]
Computer Physics Communications, 2015 The Lanczos algorithm is evaluated for solving the time-independent as well as the time-dependent Dirac equation with arbitrary electromagnetic fields. We demonstrate that the Lanczos algorithm can yield very precise eigenenergies and allows very precise time propagation of relativistic wave packets.
Randolf Beerwerth, Heiko Bauke
openaire +5 more sources
Advanced Computing, Volume 1, Issue 1, December 2026.Numerical concepts of quantum mechanics are often realized on supercomputers. Today, high‐performance computing employs triple‐hybrid schemes of MPI, CPU‐openMP, and GPU‐openMP. The present article sketches how such a scheme could be utilized in the field of quantum magnetism. ABSTRACT Lanczos concepts are often realized on supercomputers.
Jürgen Schnack
wiley +1 more source
Symmetry-resolved Krylov complexity and the uncoloured tensor model
Journal of High Energy PhysicsThe symmetry-resolved Krylov complexity is a useful tool for studying the chaotic properties of systems endowed with symmetries. We investigate the conditions under which an invariant Hermitian operator would have the symmetry-resolved Krylov complexity ...
Shaliya Kotta, P. N. Bala Subramanian
doaj +1 more source
Extending quasi-GMRES method to solve generalized Sylvester tensor equations via the Einstein product [PDF]
Iranian Journal of Numerical Analysis and OptimizationThis paper aims to extend a Krylov subspace technique based on an in-complete orthogonalization of Krylov tensors (as a multidimensional exten-sion of the common Krylov vectors) to solve generalized Sylvester tensor equations via the Einstein product ...
M.M. Izadkhah
doaj +1 more source
A Geometric Multigrid Method for 3D Magnetotelluric Forward Modeling Using Finite-Element Method
Remote Sensing, 2023 The traditional three-dimensional (3D) magnetotelluric (MT) forward modeling using Krylov subspace algorithms has the problem of low modeling efficiency.
Xianyang Huang +8 more
doaj +1 more source
Data‐Driven Spectral Prediction for Accelerating Large‐Scale Electronic Structure Calculations
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT Simulating large molecular systems comprising thousands of atoms requires highly scalable methodologies. While modern Density Functional Theory (DFT) codes exhibit linear scaling, solving the associated large, sparse generalized eigenproblems remains a critical computational bottleneck on exascale architectures.
Abhiram Badrinarayanan +6 more
wiley +1 more source
A conjugate-gradient-type rational Krylov subspace method for ill-posed problems [PDF]
, 2019 Conjugated gradients on the normal equation (CGNE) is a popular method to regularise linear inverse problems. The idea of the method can be summarized as minimising the residuum over a suitable Krylov subspace.
Grimm, Volker
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Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT For complex geometries, the coarse problem of geometric multigrid can be too large to be solved by a direct solver. Here, we report on the use of domain decomposition applied to the multigrid coarse problem. Additive overlapping Schwarz methods are domain decomposition methods for the iterative solution of partial differential equations whose ...
Stephan Köhler, Oliver Rheinbach
wiley +1 more source
Augmented unprojected Krylov subspace methods
, 2023 Augmented Krylov subspace methods aid in accelerating the convergence of a standard Krylov subspace method by including additional vectors in the search space. A residual projection framework based on residual (Petrov-) Galerkin constraints was presented
Soodhalter, Kirk M., Burke, Liam
core