Introduction to Numerical Analysis
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Each is checked against this paper’s own text: does it say what the citing paper says it does?
Conventional numerical methods for this boundary-value problem convert it into nonlinear algebraic equations and degrade rapidly as the ODE dimension grows, failing even at moderate dimensions.
“As discussed above, all conventional numerical methods for this BVP convert it into that of solving a set of nonlinear equations.As a result, all these methods suffer a rapidly decreasing performance as the dimension of the ODE increases, failing even for moderately large dimensions.”
From Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems (2015) · cites this paper as [30]
Conventional numerical solvers for the brachistochrone boundary-value problem fail without a sufficiently good initial guess, and even two-qubit systems cannot be solved from a random guess.
“These search methods fail unless provided with a sufficiently good initial guess.Even for systems as small as two qubits, a random guess is insufficient, with the result that the QBE has been solved only for special cases that possess analytic solutions [32][33][34].”
From Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems (2015) · cites this paper as [30]
Cited by
Sorted by citations
NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
Vicentini, F., Hofmann, D., Szabó, A., Wu, D., Roth, C., Giuliani, C., Pescia, G., Nys, J., Vargas-Calderón, V., Astrakhantsev, N., et al. (2022) · SciPost Physics Codebases · doi:10.21468/scipostphyscodeb.7 · Cited by 135 · see citing works
Wang, X., Allegra, M., Jacobs, K., Lloyd, S., Lupo, C., & Mohseni, M. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.170501 · Cited by 111 · see citing works
Optimal sampling time selection for parameter estimation in dynamic pathway modeling
Kutalik, Z., Cho, K.-H., & Wolkenhauer, O. (2004) · Biosystems · doi:10.1016/j.biosystems.2004.03.007 · Cited by 79 · see citing works
- Authors
- Stoer, J., & Bulirsch, R.
- Affiliations
- University of Würzburg (DE)
- Technical University of Munich (DE)
- Venue
- Texts in Applied Mathematics
- Publisher
- Springer New York
- Published
- 2002
- ISSN
- 0939-2475 (ISSN-L)
- OpenAlex
- W4301866048
- Cited by
- 1,562
- References
- 0
- Citations by year
- 2026: 41 · 2025: 49 · 2024: 44 · 2023: 70 · 2022: 105 · 2021: 113 · 2020: 90 · 2019: 65 · 2018: 82 · 2017: 79 · 2016: 87 · 2015: 91 · 2014: 85 · 2013: 81 · 2012: 100
- FWCI
- 18.24
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- Locations
- Texts in applied mathematics (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical and Computational Methods
- Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Keywords
- numerical analysis, mathematical modeling, scientific computing, interdisciplinary applications of mathematics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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