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Artykuły w czasopismach na temat "Rounding error analysis"
Connolly, Michael P., i Nicholas J. Higham. "Probabilistic Rounding Error Analysis of Householder QR Factorization". SIAM Journal on Matrix Analysis and Applications 44, nr 3 (28.07.2023): 1146–63. http://dx.doi.org/10.1137/22m1514817.
Pełny tekst źródłaKolomys, Olena, i Liliya Luts. "Algorithm for Calculating Primary Spectral Density Estimates Using FFT and Analysis of its Accuracy". Cybernetics and Computer Technologies, nr 2 (30.09.2022): 52–57. http://dx.doi.org/10.34229/2707-451x.22.2.5.
Pełny tekst źródłaConnolly, Michael P., Nicholas J. Higham i Theo Mary. "Stochastic Rounding and Its Probabilistic Backward Error Analysis". SIAM Journal on Scientific Computing 43, nr 1 (styczeń 2021): A566—A585. http://dx.doi.org/10.1137/20m1334796.
Pełny tekst źródłaCuyt, Annie, i Paul Van der Cruyssen. "Rounding error analysis for forward continued fraction algorithms". Computers & Mathematics with Applications 11, nr 6 (czerwiec 1985): 541–64. http://dx.doi.org/10.1016/0898-1221(85)90037-9.
Pełny tekst źródłaHigham, Nicholas J., i Theo Mary. "A New Approach to Probabilistic Rounding Error Analysis". SIAM Journal on Scientific Computing 41, nr 5 (styczeń 2019): A2815—A2835. http://dx.doi.org/10.1137/18m1226312.
Pełny tekst źródłaZou, Qinmeng. "Probabilistic Rounding Error Analysis of Modified Gram–Schmidt". SIAM Journal on Matrix Analysis and Applications 45, nr 2 (21.05.2024): 1076–88. http://dx.doi.org/10.1137/23m1585817.
Pełny tekst źródłaMezzarobba, Marc. "Rounding error analysis of linear recurrences using generating series". ETNA - Electronic Transactions on Numerical Analysis 58 (2023): 196–227. http://dx.doi.org/10.1553/etna_vol58s196.
Pełny tekst źródłaKiełbasiński, Andrzej. "A note on rounding-error analysis of Cholesky factorization". Linear Algebra and its Applications 88-89 (kwiecień 1987): 487–94. http://dx.doi.org/10.1016/0024-3795(87)90121-2.
Pełny tekst źródłaJournal, Baghdad Science. "A Note on the Perturbation of arithmetic expressions". Baghdad Science Journal 13, nr 1 (6.03.2016): 190–97. http://dx.doi.org/10.21123/bsj.13.1.190-197.
Pełny tekst źródłaRudikov, D. A., i A. S. Ilinykh. "Error analysis of the cutting machine step adjustable drive". Journal of Physics: Conference Series 2131, nr 2 (1.12.2021): 022046. http://dx.doi.org/10.1088/1742-6596/2131/2/022046.
Pełny tekst źródłaRozprawy doktorskie na temat "Rounding error analysis"
Plet, Antoine. "Contribution to error analysis of algorithms in floating-point arithmetic". Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEN038/document.
Pełny tekst źródłaFloating-point arithmetic is an approximation of real arithmetic in which each operation may introduce a rounding error. The IEEE 754 standard requires elementary operations to be as accurate as possible. However, through a computation, rounding errors may accumulate and lead to totally wrong results. It happens for example with an expression as simple as ab + cd for which the naive algorithm sometimes returns a result with a relative error larger than 1. Thus, it is important to analyze algorithms in floating-point arithmetic to understand as thoroughly as possible the generated error. In this thesis, we are interested in the analysis of small building blocks of numerical computing, for which we look for sharp error bounds on the relative error. For this kind of building blocks, in base and precision p, we often successfully prove error bounds of the form α·u + o(u²) where α > 0 and u = 1/2·β1-p is the unit roundoff. To characterize the sharpness of such a bound, one can provide numerical examples for the standard precisions that are close to the bound, or examples that are parametrized by the precision and generate an error of the same form α·u + o(u²), thus proving the asymptotic optimality of the bound. However, the paper and pencil checking of such parametrized examples is a tedious and error-prone task. We worked on the formalization of a symbolicfloating-point arithmetic, over numbers that are parametrized by the precision, and implemented it as a library in the Maple computer algebra system. We also worked on the error analysis of the basic operations for complex numbers in floating-point arithmetic. We proved a very sharp error bound for an algorithm for the inversion of a complex number in floating-point arithmetic. This result suggests that the computation of a complex division according to x/y = (1/y)·x may be preferred, instead of the more classical formula x/y = (x·y)/|y|². Indeed, for any complex multiplication algorithm, the error bound is smaller with the algorithms described by the “inverse and multiply” approach.This is a joint work with my PhD advisors, with the collaboration of Claude-Pierre Jeannerod (CR Inria in AriC, at LIP)
Chesneaux, Jean-Marie. "Etude theorique et implementation en ada de la methode cestac". Paris 6, 1988. http://www.theses.fr/1988PA066143.
Pełny tekst źródłaGerest, Matthieu. "Using Block Low-Rank compression in mixed precision for sparse direct linear solvers". Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS447.
Pełny tekst źródłaIn order to solve large sparse linear systems, one may want to use a direct method, numerically robust but rather costly, both in terms of memory consumption and computation time. The multifrontal method belong to this class algorithms, and one of its high-performance parallel implementation is the solver MUMPS. One of the functionalities of MUMPS is the use of Block Low-Rank (BLR) matrix compression, that improves its performance. In this thesis, we present several new techniques aiming at further improving the performance of dense and sparse direct solvers, on top of using a BLR compression. In particular, we propose a new variant of BLR compression in which several floating-point formats are used simultaneously (mixed precision). Our approach is based on an error analysis, and it first allows to reduce the estimated cost of a LU factorization of a dense matrix, without having a significant impact on the error. Second, we adapt these algorithms to the multifrontal method. A first implementation uses our mixed-precision BLR compression as a storage format only, thus allowing to reduce the memory footprint of MUMPS. A second implementation allows to combine these memory gains with time reductions in the triangular solution phase, by switching computations to low precision. However, we notice performance issues related to BLR for this phase, in case the system has many right-hand sides. Therefore, we propose new BLR variants of triangular solution that improve the data locality and reduce data movements, as highlighted by a communication volume analysis. We implement our algorithms within a simplified prototype and within solver MUMPS. In both cases, we obtain time gains
Damouche, Nasrine. "Improving the Numerical Accuracy of Floating-Point Programs with Automatic Code Transformation Methods". Thesis, Perpignan, 2016. http://www.theses.fr/2016PERP0032/document.
Pełny tekst źródłaCritical software based on floating-point arithmetic requires rigorous verification and validation process to improve our confidence in their reliability and their safety. Unfortunately available techniques for this task often provide overestimates of the round-off errors. We can cite Arian 5, Patriot rocket as well-known examples of disasters. These last years, several techniques have been proposed concerning the transformation of arithmetic expressions in order to improve their numerical accuracy and, in this work, we go one step further by automatically transforming larger pieces of code containing assignments, control structures and functions. We define a set of transformation rules allowing the generation, under certain conditions and in polynomial time, of larger expressions by performing limited formal computations, possibly among several iterations of a loop. These larger expressions are better suited to improve, by re-parsing, the numerical accuracy of the program results. We use abstract interpretation based static analysis techniques to over-approximate the round-off errors in programs and during the transformation of expressions. A tool has been implemented and experimental results are presented concerning classical numerical algorithms and algorithms for embedded systems
Książki na temat "Rounding error analysis"
Wilkinson, J. H. Rounding errors in algebraic processes. New York: Dover, 1994.
Znajdź pełny tekst źródłaLemeshko, Boris. Nonparametric consent criteria. ru: INFRA-M Academic Publishing LLC., 2023. http://dx.doi.org/10.12737/2058731.
Pełny tekst źródłaLemeshko, Boris, Aleksandr Popov i Vadim Seleznev. Criteria for checking the deviation of the distribution from the normal law. Application Guide. ru: INFRA-M Academic Publishing LLC., 2022. http://dx.doi.org/10.12737/1896110.
Pełny tekst źródłaCzęści książek na temat "Rounding error analysis"
Isychev, Anastasia, i Eva Darulova. "Scaling up Roundoff Analysis of Functional Data Structure Programs". W Static Analysis, 371–402. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-44245-2_17.
Pełny tekst źródłaHartmanns, Arnd. "Correct Probabilistic Model Checking with Floating-Point Arithmetic". W Tools and Algorithms for the Construction and Analysis of Systems, 41–59. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99527-0_3.
Pełny tekst źródła"Part IV Rounding Error". W Numerical Analysis, 167. Society for Industrial and Applied Mathematics, 1990. http://dx.doi.org/10.1137/1.9781611971323.pt4.
Pełny tekst źródła"9. Rounding Error for Gaussian Elimination". W Numerical Analysis, 169–93. Society for Industrial and Applied Mathematics, 1990. http://dx.doi.org/10.1137/1.9781611971323.ch9.
Pełny tekst źródłaFrechtling, Michael, i Philip H. W. Leong. "An FPGA-Based Floating Point Unit for Rounding Error Analysis". W Transforming Reconfigurable Systems, 39–56. IMPERIAL COLLEGE PRESS, 2015. http://dx.doi.org/10.1142/9781783266975_0003.
Pełny tekst źródłaGaroche, Pierre-Loïc. "Floating-point Semantics of Analyzed Programs". W Formal Verification of Control System Software, 167–90. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691181301.003.0009.
Pełny tekst źródłaOlver, F. W. J. "Rounding errors in algebraic processes¬ in level-index arithmetic". W Reliable Numerical Commputation, 197–206. Oxford University PressOxford, 1990. http://dx.doi.org/10.1093/oso/9780198535645.003.0012.
Pełny tekst źródłaKurz, V., i F. Stummel. "Rounding Error Analysis of Elimination Methods for Unsymmetric Two-Point Boundary Value Problems". W Zeitschrift für Angewandte Mathematik und Mechanik Volume 66, Number 5, 415–17. De Gruyter, 1986. http://dx.doi.org/10.1515/9783112550946-063.
Pełny tekst źródłaEarl, Richard. "Should I believe my computer?" W Mathematical Analysis: A Very Short Introduction, 65–82. Oxford University PressOxford, 2023. http://dx.doi.org/10.1093/actrade/9780198868910.003.0004.
Pełny tekst źródłaSteiner, Erich. "Numerical methods". W The Chemistry Maths Book. Oxford University Press, 2008. http://dx.doi.org/10.1093/hesc/9780199205356.003.0020.
Pełny tekst źródłaStreszczenia konferencji na temat "Rounding error analysis"
Kellison, Ariel, Mohit Tekriwal, Jean-Baptiste Jeannin i Geoffrey Hulette. "Towards Verified Rounding Error Analysis for Stationary Iterative Methods". W 2022 IEEE/ACM Sixth International Workshop on Software Correctness for HPC Applications (Correctness). IEEE, 2022. http://dx.doi.org/10.1109/correctness56720.2022.00007.
Pełny tekst źródłaHolý, Vladimír. "How big is the rounding error in financial high-frequency data?" W INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044146.
Pełny tekst źródłaIwahashi, Masahiro, i Hitoshi Kiya. "Finite word length error analysis based on basic formula of rounding operation". W 2008 International Symposium on Intelligent Signal Processing and Communications Systems (ISPACS 2008). IEEE, 2009. http://dx.doi.org/10.1109/ispacs.2009.4806763.
Pełny tekst źródłaWei, Ming, Yonghong Wang i Huafen Song. "Sensitivity Analysis and Numerical Stability Analysis of the Algorithms for Predicting the Performance of Turbines". W ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-94482.
Pełny tekst źródłaGao, Ming, i Ravi Krishnamurthy. "Investigate Performance of Current In-Line Inspection Technologies for Dents and Dent Associated With Metal Loss Damage Detection". W 2010 8th International Pipeline Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ipc2010-31409.
Pełny tekst źródłaNeuhäuser, Karl, i Rudibert King. "Robust Active Flow Control of a Stator Cascade With Integer Control Functions and Sum-Up Rounding". W ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-91249.
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