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Some methods of speeding up the convergence of iteration methods
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In the citing paper
“Example 1.1 (Heavy-ball momentum gradient descent; Polyak [54]) . This optimizer can be written in the form (1) with”
From How Memory in Optimization Algorithms Implicitly Modifies the Loss (2025) · cites this paper as [54]
In the citing paper
“For example, gradient descent with momentum has exponentially decaying memory through exponentially averaged past gradients.”
From How Memory in Optimization Algorithms Implicitly Modifies the Loss (2025) · cites this paper as [54]
Citations
Cites
No references could be resolved yet.
Research works printed but not linked: 7
- Kantorovich, 1956, Approximate solution of functional equations, Uspekhi Mat. Nauk, 11, 99
- Gavurin, 1958, Nonlinear functional equations and continuous analogues of iterative methods, Izv. VUZov. Ser. Mat., 5, 18
- Buledz, 1961, The problem of speeding up the convergence of iteration processes in the approximate solution of linear operational equations, Dop. Akad. Nauk SSSR, 3, 265
- Frankel, 1950, Convergence rates of iterative treatments of partial differential equations, Math. Tables and Other Aids Comput., 4, 65, 10.2307/2002770 · DOI
- Polyak, 1963, Gradient methods for minimizing functionals, Zh. vych. mat., 3, 643
- Gel'fand, 1961, Principles of nonlocal search in systems of automatic optimization, Dokl. Akad. Nauk SSSR, 137, 295
- Inomata, 1961, On the golf method, Bu l. Electrotec. Lab., 25, 495
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Metadata
- Authors
- Polyak, B. T.
- Corresponding author
- Polyak, B.T.
- ORCID
- Polyak, B.T.
- Venue
- USSR Computational Mathematics and Mathematical Physics
- Publisher
- Elsevier BV
- Published
- 1964-01
- Volume
- 4
- Issue
- 5
- Pages
- 1-17
- ISSN
- 0041-5553 (ISSN-L)
- OpenAlex
- W1988720110
- Cited by
- 3,069
- References
- 0
- Citations by year
- 2026: 345 · 2025: 426 · 2024: 368 · 2023: 354 · 2022: 313 · 2021: 389 · 2020: 301 · 2019: 234 · 2018: 124 · 2017: 87 · 2016: 58 · 2015: 33 · 2014: 11 · 2013: 3 · 2012: 3
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- USSR Computational Mathematics and Mathematical Physics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Numerical Analysis › Iterative Methods for Nonlinear Equations
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Optimization and Variational Analysis
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Keywords
- convergence acceleration, iterative methods, multistep methods, Banach space operators, functional equations, ordinary differential equations, convergence rate, successive approximations, Hilbert spaces
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- This page
- CoChat. (2026). Citation check: Some methods of speeding up the convergence of iteration methods. https://app.cochat.ai/papers/10.1016/0041-5553(64)90137-5
- The paper
- Polyak, B. T. (1964). Some methods of speeding up the convergence of iteration methods. USSR Computational Mathematics and Mathematical Physics. https://doi.org/10.1016/0041-5553(64)90137-5
