Iterative solution of linear systems in the 20th century

By Y. Saad, Henk A. van der Vorst. 2000

513 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2cfa6c012ba179606b6fc27d8fc8d8fccb90806d

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Iterative Krylov Methods for Large Linear Systems (2003, methodology): “Online Iterative Krylov Methods for Large Linear Systems (Cambridge Monographs on Applied and Computational Mathematics) by Henk A. van der Vorst ebook PDF download Iterative Krylov Methods for Large Linear Systems (Cambridge Monographs on Applied and Computational Mathematics) by Henk A. van der Vo”
A fast 3D dual boundary element method based on hierarchical matrices (2008, background): “The importance of the subject has also been stressed by Saad and van der Vorst (2000), in their survey of iterative solvers for linear systems.”
Preconditioning techniques for large linear systems: a survey (2002, background): “For more detailed information, the interested reader should consult Golub and O’Leary [155] (for developments up to 1976), the papers by Hestenes and by Young in [224] (for early work on conjugate gradients and SOR, respectively), and the recent overview by Saad and van der Vorst [255].”
Geometric aspects of the theory of Krylov subspace methods (2001, unknown): “In addition, there are also several survey papers with differing emphases, among which we mention those of Ashby, Manteuffel and Saylor (1990), Freund, Golub and Nachtigal (1992), Gutknecht (1997), Golub and van der Vorst (1997) and van der Vorst and Saad (2000).”
Accurate diagnosis of conformal arrays from near-field data using the matrix method (2005, background): “The inversion of large linear systems is a deeply investigated subject, and many algorithms have been proposed in literature [16].”
Jacobian-free Newton-Krylov methods: a survey of approaches and applications (2004, unknown): “A wide variety of iterative methods fall within the Krylov taxonomy [11,84,157] and there are numerous recent survey papers in this area [71,146,159].”
Automatic performance tuning of sparse matrix kernels (2003, background): “These costs are acceptable in important application contexts like solving linear systems or computing eigenvalues by iterative methods, where hundreds (or more) of SpMVs can be required for a given matrix [30, 177, 94, 65, 269].”
Recent computational developments in Krylov subspace methods for linear systems (2007, methodology): “For a historical perspective on the development of these methods, see [276].”