Iterative methods for sparse linear systems

By Y. Saad. 2003

15,600 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Computational Theory and Mathematics

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In Atomic and Molecular Physics, and Optics

In Computational Mechanics

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Citations in the corpus

Data Encoding for Byzantine-Resilient Distributed Optimization (2019, methodology): “; (ii) iterative methods for solving sparse linear systems [60]; (iii) many graph algorithms, where the graph is represented by a fixed adjacency matrix, [61].”
Should one compute the Temporal Difference fix point or minimize the Bellman Residual? The unified oblique projection view (2010, background): “We have discussed the close relations of our results with those of Schoknecht (2002) and Yu & Bertsekas (2008), and argued that our work simplifies and extends them.”
INEXACT AND TRUNCATED PARAREAL-INTIME KRYLOV SUBSPACE METHODS FOR PARABOLIC OPTIMAL CONTROL PROBLEMS (2012, methodology): “1Truncated FOM is called IOM in [26] and it can be implemented in such a way that um = u0 + Vmxm is computed directly from um−1 without the need to store all the vectors in Vm.”
Parallel Lagrange-Newton-Krylov-Schur Methods for PDE-Constrained Optimization. Part I: The Krylov-Schur Solver (2005, methodology): “The performance of a Krylov method depends highly on the preconditioned operator spectrum [21, 36].”
Krylov Subspace Methods for Linear Systems with Tensor Product Structure (2010, neutral): “[21]).”
A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control (2013, methodology): “This can be achieved using e.g. Arnoldi or Lanczos algorithms (explanation of these algorithms and implementation details are given in [60]).”
Sourcebook of parallel computing (2003, background): “[564], Morton and Mayers [690], Quarteroni and Valli [784], Saad [820], and Smith et al.”
GMRES, L-Curves, and Discrete Ill-Posed Problems (2002, methodology): “The GMRES method and the condition L-curve The GMRES method of Saad and Schultz [15] [16] is based on the Arnoldi process.”
Interactive local adjustment of tonal values (2006, background): “The resulting factor matrix is then used as the preconditioner in all subsequent invocations of PCG.”
X-ray tomographic and hydraulic characterization of burrowing by three earthworm species in repacked soil cores (2003, methodology): “This system of equations was solved by a classical Cholesky decomposition (Saad, 1996).”