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Review of fast square root calculation methods for fixed point microcontroller-based control systems of power electronics
2020
International Journal of Power Electronics and Drive Systems (IJPEDS)
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The maximum relative error of the proposed method is 3.36% for calculation without division, and can be decreased to 0.055% using one division operation. ...
Taking into account that for many applications approximate calculation of a square root is enough, calculation time can be decreased with the price of precision of calculation. ...
error is: As can be seen from (40), the error is negative, so initial guess x 0 can be improved by adding shift. ...
doi:10.11591/ijpeds.v11.i3.pp1153-1164
fatcat:wnnkz7nr7ncbdalakn4xvlf34m
The constructive reals as a Java library
2005
The Journal of Logic and Algebraic Programming
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We hope to demonstrate that even such a basic implementation of constructive real arithmetic can be useful in a number of contexts, including in a desk calculator utility distributed with the package. ...
A secondary goal was to demonstrate that some second-order functions on the reals, such as restricted inverse and derivative operations, can be implemented with sufficient performance to be useful. ...
The division by 4 is necessary to adjust for the implicit scaling. ...
doi:10.1016/j.jlap.2004.07.002
fatcat:f5y4cxadynbyphwbkg4idd7rca
Extensions: Improving the Poisson Solver
[chapter]
2016
Solving PDEs in Python
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errors and convergence rates. 109 ...
We will also discuss how to utilize iterative solvers with preconditioners for solving linear systems, how to compute derived quantities, such as, e.g., the flux on a part of the boundary, and how to compute ...
Computing convergence rates A central question for any numerical method is its convergence rate: how fast does the error approach zero when the resolution is increased? ...
doi:10.1007/978-3-319-52462-7_5
fatcat:ud4ebqp4fnev3kskrb3ziqabuy
Wireless Quantized Federated Learning: A Joint Computation and Communication Design
[article]
2022
arXiv
pre-print
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Moreover, the proposed method is shown to result in faster convergence in comparison with baseline schemes. Finally, useful insights for the selection of the quantization error tolerance are provided. ...
More specifically, the convergence analysis of the FL algorithm with stochastic quantization is firstly presented, which reveals the impact of the quantization error on the convergence rate. ...
We made this choice, since for different tolerance values, the duration of a global round also varies. ...
arXiv:2203.05878v1
fatcat:7cgbytk36ndtrnbaninjimsfza
The Influence of the Exact Evaluation of Radiation Fields in Finite Precision Arithmetic on the Stability of the Time Domain Integral Equation Method
2013
IEEE Transactions on Antennas and Propagation
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Hence, a reformulation is necessary to remove the singular behavior and obtain the robustness required for industrial application. ...
Transient electromagnetic scattering phenomena can effectively be simulated with time domain integral equation methods. ...
(d) The convergence of the error in the robust formulation w.r.t. the tolerance value.
Fig. 9. Tolerance regions with , for a triangle given by vertices ([0, 0], [2, 0], [0, 0.4]) and . ...
doi:10.1109/tap.2013.2281365
fatcat:6rmlwizadra6dm7r3xivlkmh6a
Page 3242 of Mathematical Reviews Vol. , Issue 87f
[page]
1987
Mathematical Reviews
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
The proven error estimations are illustrated by some numerical examples, and hints for improvements are given. K. ...
The 5th principal root of the matrix can be found using the algorithm presented with an error tolerance of 10~?° in 10 iterations. E. L. Yip (Seattle, Wash.) ...
Numerical implementation of the QMR algorithm by using discrete stochastic arithmetic
2005
Journal of Applied Mathematics and Computing
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In each step of the quasi-minimal residual (QMR) method which uses a look-ahead variant of the nonsymmetric Lanczos process to generate basis vectors for the Krylov subspaces induced by A, it is necessary ...
QMR method with the estimation of the accuracy of some intermediate results. ...
Chesneaux, and the anonymous referee for advise on many aspects of this work. ...
doi:10.1007/bf02936068
fatcat:gf4zgatu2zenrj3u6qibiajq3e
Self-organized aggregation in irregular wireless networks
2010
2010 IFIP Wireless Days
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We evaluate our approach by simulation on sparse, irregular graphs with low expansion for the simplified system model. ...
Aggregates are calculated only over nodes placed in the vicinity, and nodes communicate only with their immediate neighbors by using a wireless broadcast. ...
One approach to improving fault tolerance in dynamic distributed systems, which is measured by the maximum radius of impact caused by a given fault, is presented by S. Pike [21] . ...
doi:10.1109/wd.2010.5657705
dblp:conf/wd/GeibigB10
fatcat:ybjhguyhprdhtiab3vd35iswre
FHDnn
2022
Proceedings of the 59th ACM/IEEE Design Automation Conference
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Compared to CNNs, we show through experiments that FHDnn reduces communication costs by 66×, local client compute and energy consumption by 1.5 -6×, while being highly robust to network errors with minimal ...
errors by avoiding the transmission of the CNN and training only the hyperdimensional component. ...
Acknowledgements This work was supported in part by CRISP, one of six centers in JUMP (an SRC program sponsored by DARPA), SRC Global Research Collaboration (GRC) grant, and NSF grants #1911095, #1826967 ...
doi:10.1145/3489517.3530394
fatcat:spcdbhhlwzfrniyfwz3oml5xl4
nlstac: Non-Gradient Separable Nonlinear Least Squares Fitting
2023
The R Journal
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2024 pre-print arXiv:2402.04124v1 fatcat:hzeqv7vfavbb7pulh7vlqgel7y
Even though convergence for this method is guaranteed for exponential decay using the max-norm, the algorithm exhibits remarkable robustness, and its use has been extended to a wide range of functions ...
A new package for nonlinear least squares fitting is introduced in this paper. ...
to improve those values-and the achieved convergence tolerance is 1.391929×10 Note that all outputs coincide for both methods. ...
doi:10.32614/rj-2023-040
fatcat:yx2feondobe2bfl3ljo6vbpmmu
An Integrated Multicriterionhp-Adaptive Pseudospectral Method for Direct Optimal Control Problems Solving
2012
Mathematical Problems in Engineering
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It is challenging to improve the convergence rate, the solution accuracy, and the applicability of PMs, especially for nonsmooth problems. ...
In this paper, we propose a novel method which integrates multicriterion tohp-adaptive PM, in order to further improve the performance. ...
Acknowledgments Great thanks go to the reviewers for valuable comments on our revision of the paper. ...
doi:10.1155/2012/760890
fatcat:srlqalrd6zegdeeakyas2gebla
General framework for re-assuring numerical reliability in parallel Krylov solvers: A case of BiCGStab methods
[article]
2023
arXiv
pre-print
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This paper proposes a general framework for deriving reproducible and accurate variants of Krylov subspace methods. ...
The framework is illustrated on the preconditioned BiCGStab method and its pipelined modification, which in fact is a distinctive method from the Krylov subspace family, for the solution of non-symmetric ...
The research from Universitat Jaume I was funded by the project PID2020-113656RB-C21 via MCIN/AEI/10.13039/501100011033 and project UJI-B2021-58. ...
arXiv:2302.04180v1
fatcat:qpacm36n2vbyfjcrzhraoo2soy
Performance Analysis for Resource Constrained Decentralized Federated Learning Over Wireless Networks
[article]
2023
arXiv
pre-print
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For analog transmission, we discuss the impact of channel fading and noise on the model performance and the maximum errors accumulation with convergence guarantee over fading channels. ...
Our simulation results validate our analysis and discussion, revealing how to improve performance by optimizing system parameters under different communication conditions. ...
The maximum error in one communication round that DFL can tolerate is given by the following corollary. ...
arXiv:2308.06496v1
fatcat:42gcmdbcxvha3m7d5x4mfjrpnq
Aphmesh refinement method for optimal control
2014
Optimal control applications & methods
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with fixed-order methods. ...
The process of refining the mesh is repeated until a specified relative error tolerance is met. ...
Acknowledgments The authors gratefully acknowledge support for this research from the U.S. Office of Naval Research under Grant N00014-11-1-0068 and from the U.S. ...
doi:10.1002/oca.2114
fatcat:jy7e5kyh3rfexcm77lefabjicy
AISC: Approximate Instruction Set Computer
[article]
2018
arXiv
pre-print
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At the same time, the energy efficiency of computing can improve by exploiting algorithmic noise tolerance: by mapping code sequences that can tolerate (any potential inaccuracy induced by) the incomplete ...
This paper makes the case for a single-ISA heterogeneous computing platform, AISC, where each compute engine (be it a core or an accelerator) supports a different subset of the very same ISA. ...
For example, under Depth, applications that tolerate instruction dropping either compensate for the missing instructions by executing more to meet the convergence criteria, or exhibit a very large accuracy ...
arXiv:1803.06955v1
fatcat:lw2arxhptzegbbo7tiqmkrluv4
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