The DOI matches its Crossref record.
Numerical Methods for Large Eigenvalue Problems: Revised Edition
Abstract
Preface to the Classics Edition Preface 1. Background in matrix theory and linear algebra 2. Sparse matrices 3. Perturbation theory and error analysis 4. The tools of spectral approximation 5. Subspace iteration 6. Krylov subspace methods 7. Filtering and restarting techniques 8. Preconditioning techniques 9. Non-standard eigenvalue problems 10. Origins of matrix eigenvalue problems References Index.
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“A variational quantum circuit for CO that is not derived from QAOA or VQE is represented by a quantum version of the shifted power method [211], where the rationale is based on finding the dominant eigenpair of a matrix [36].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [211]
Citations
Cited by
Sorted by citations
Iterative Methods for Sparse Linear Systems
Saad, Y. E.-M. (2003) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898718003 · Cited by 13,931
Self-citationA variational eigenvalue solver on a photonic quantum processor
Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014) · Nature Communications · doi:10.1038/ncomms5213 · Cited by 4,552
IEEE Transactions on Pattern Analysis and Machine Intelligence
(2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.1307293 · Cited by 3,708
Ab initio molecular simulations with numeric atom-centered orbitals
Blüm, V., Gehrke, R., Hanke, F., Havu, P., Havu, V., Ren, X., Reuter, K., & Scheffler, M. (2009) · Computer Physics Communications · doi:10.1016/j.cpc.2009.06.022 · Cited by 2,924
Fast linear iterations for distributed averaging
Xiao, L., & Boyd, S. (2004) · Systems & Control Letters · doi:10.1016/j.sysconle.2004.02.022 · Cited by 2,734
Metadata
- Authors
- Saad, Y.
- Affiliations
- University of Minnesota (US)
- Corresponding author
- Saad, Yousef
- ORCID
- Saad, Yousef
- Venue
- Society for Industrial and Applied Mathematics eBooks
- Published
- 2011-01-01
- OpenAlex
- W1563653928
- Cited by
- 2,364
- References
- 0
- Citations by year
- 2026: 80 · 2025: 92 · 2024: 88 · 2023: 88 · 2022: 92 · 2021: 119 · 2020: 118 · 2019: 124 · 2018: 134 · 2017: 107 · 2016: 100 · 2015: 100 · 2014: 130 · 2013: 82 · 2012: 70
- FWCI
- 28.30
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Society for Industrial and Applied Mathematics eBooks (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Physical Sciences › Engineering › Computational Mechanics › Advanced Numerical Methods in Computational Mathematics
- Keywords
- large eigenvalue problems, matrix eigenvalue problems, sparse matrices, perturbation theory, error analysis, spectral approximation, subspace iteration, Krylov subspace methods, restarting, filtering, preconditioning
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