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Certified Roundoff Error Bounds Using Semidefinite Programming. [PDF]
ACM Transactions on Mathematical Software, 2015 Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs or custom ...
Constantinides, GA +2 more
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QR Decomposition Based on Double-double Precision Gram-Schmidt Orthogonalization Method [PDF]
Jisuanji kexue, 2023 The Gram-Schmidt orthogonalization algorithm and its related modified algorithms often show numerical instability when computing ill-conditioned or large-scale matrices.To solve this problem,this paper explores the cumulative effect of round-off errors ...
JIN Jiexi, XIE Hehu, DU Peibing, QUAN Zhe, JIANG Hao
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Mathematical modeling of parameter identification process of convection-diffusion transport models using the SVD-based Kalman filter [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 The paper addresses a problem of mathematical modeling of the process of identifying the coefficients of a partial differential equation in convection-diffusion transport models based on the results of noisy measurements of the function values ...
Anastasia N. Kuvshinova +2 more
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Mathematics, 2021 For large-scale problems, how to establish an algorithm with high accuracy and stability is particularly important. In this paper, the Householder bidiagonalization total least squares (HBITLS) algorithm and nonlinear iterative partial least squares for ...
Zhanshan Yang, Xilan Liu
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Global error estimation of linear multistep methods through the Runge-Kutta methods [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2016 In this paper, we study the global truncation error of the linear multistep methods (LMM) in terms of local truncation error of the corresponding Runge-Kutta schemes. The key idea is the representation of LMM with a corresponding Runge-Kutta method.
Javad Farzi
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Axioms, 2023 This paper is presented in the context of sensitivity analysis (SA) of large-scale data assimilation (DA) models. We studied consistency, convergence, stability and roundoff error propagation of the reduced-space optimization technique arising in ...
Luisa D’Amore, Rosalba Cacciapuoti
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Where the really hard problems aren’t
Operations Research Perspectives, 2020 Not all problem instances in combinatorial optimization are equally hard. One famous study “Where the Really Hard Problems Are” shows that for three decision problems and one optimization problem, computational costs can vary dramatically for equally ...
Joeri Sleegers +3 more
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Error Analysis of Band Matrix Method [PDF]
, 1984 Numerical error in the solution of the band matrix method based on the elimination method in single precision is investigated theoretically and experimentally, and the behaviour of the truncation error and the roundoff error is clarified.
Soga, Akira, Taniguchi, Takeo
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Propagation of internal errors in explicit Runge--Kutta methods and internal stability of SSP and extrapolation methods [PDF]
, 2014 In practical computation with Runge--Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth.
Ketcheson, David I. +2 more
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General moments of roundoff error [PDF]
Communications in Statistics - Simulation and Computation, 2019 Li and Nadarajah [Signal Processing 127 (2016) 185–190] derived expressions for mean and variance of roundoff error for any continuous random variable. Here, we derive expressions for general moments of the roundoff error, allowing one to study other aspects of roundoff error than just mean and variance.
Wiegand, Martin, Nadarajah, Saralees
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