Results 11 to 20 of about 281 (133)
Krylov Subspace Estimation [PDF]
SIAM Journal on Scientific Computing, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael K. Schneider, Alan S. Willsky
openaire +4 more sources
Convergence of Restarted Krylov Subspaces to Invariant Subspaces [PDF]
SIAM Journal on Matrix Analysis and Applications, 2004 The authors prove estimates for the angle (strictly spoken: for the containment gap) between a searched invariant subspace of a general \(n\times n\) matrix and the subspace generated by Krylov subspace methods like the Arnoldi algorithm or the biorthogonal Lanczos algorithm.
Christopher Beattie +2 more
openaire +1 more source
Preconditioners for Krylov subspace methods: An overview [PDF]
GAMM-Mitteilungen, 2020 AbstractWhen simulating a mechanism from science or engineering, or an industrial process, one is frequently required to construct a mathematical model, and then resolve this model numerically. If accurate numerical solutions are necessary or desirable, this can involve solving large‐scale systems of equations.
Pearson, John W., Pestana, Jennifer
openaire +6 more sources
The Hamiltonian extended Krylov subspace method
The Electronic Journal of Linear Algebra, 2022 An algorithm for constructing a $J$-orthogonal basis of the extended Krylov subspace$\mathcal{K}_{r,s}=\operatorname{range}\{u,Hu, H^2u,$ $ \ldots, $ $H^{2r-1}u, H^{-1}u, H^{-2}u, \ldots, H^{-2s}u\},$where $H \in \mathbb{R}^{2n \times 2n}$ is a large (and sparse) Hamiltonian matrix is derived (for $r = s+1$ or $r=s$).
Peter Benner +2 more
openaire +4 more sources
Krylov Subspace Methods in Dynamical Sampling [PDF]
Sampling Theory in Signal and Image Processing, 2016 Let $B$ be an unknown linear evolution process on $\mathbb C^d\simeq l^2(\mathbb Z_d)$ driving an unknown initial state $x$ and producing the states $\{B^\ell x, \ell = 0,1,\ldots\}$ at different time levels. The problem under consideration in this paper is to find as much information as possible about $B$ and $x$ from the measurements $Y=\{x(i)$, $Bx ...
Akram Aldroubi, Ilya A. Krishtal
openaire +3 more sources
Pipelined, Flexible Krylov Subspace Methods [PDF]
SIAM Journal on Scientific Computing, 2016 We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with operator and nonlinear or nondeterministic preconditioner application.The methods are hence aimed at hiding network
Patrick Sanan +2 more
openaire +2 more sources
Partitioned Quantum Subspace Expansion [PDF]
QuantumWe present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states.
Tom O'Leary +3 more
doaj +1 more source
Parallel primal‐dual interior point method for the solution of dynamic optimal power flow
IET Generation, Transmission & Distribution, 2023 This work presents a novel solution for accelerating the dynamic optimal power flow using a distributed‐memory parallelization approach. Unlike other two‐stage relaxation‐based approaches (such as ADMM), the proposed approach constructs the entire ...
Rylee Sundermann +4 more
doaj +1 more source
S-Step BiCGStab Algorithms for Geoscience Dynamic Simulations
Oil & Gas Science and Technology, 2016 In basin and reservoir simulations, the most expensive and time consuming phase is solving systems of linear equations using Krylov subspace methods such as BiCGStab.
Anciaux-Sedrakian Ani +3 more
doaj +1 more source
Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems
International Journal of Mathematics and Mathematical Sciences, 2009 The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original ...
Mohammedi R. Abdel-Aziz +1 more
doaj +1 more source