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An Extended Quadratic Frobenius Primality Test with Average and Worst Case Error Estimates

Ivan B. Damgård, Gudmund Skovbjerg Frandsen
2003 BRICS Report Series  
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham.  ...  EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776^t for t iterations of the test in the worst case.  ...  Algorithm 1 Extended Quadratic Frobenius Test (EQFTac).  ... 
doi:10.7146/brics.v10i9.21780 fatcat:3mroku6hqbf7vncqbd76752gga

An Extended Quadratic Frobenius Primality Test with Average and Worst Case Error Estimates [chapter]

Ivan Bjerre Damgård, Gudmund Skovbjerg Frandsen
2003 Lecture Notes in Computer Science  
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham.  ...  EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776 t for t iterations of the test in the worst case.  ...  Algorithm 1 Extended Quadratic Frobenius Test (EQFTac).  ... 
doi:10.1007/978-3-540-45077-1_12 fatcat:f5axlzotzvfijlkrmfb2djk2p4

An Extended Quadratic Frobenius Primality Test with Average Case Error Estimates

Ivan B. Damgård, Gudmund Skovbjerg Frandsen
2001 BRICS Report Series  
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham.  ...  The variant has slightly larger worst case error probability than EQFT, but still improves on previous proposed tests.  ...  Algorithm 3 Extended Quadratic Frobenius Test (EQFT).  ... 
doi:10.7146/brics.v8i45.21705 fatcat:a4aug7zhnjbrjndbpkan3u2fvy

Worst-Case Linear Discriminant Analysis as Scalable Semidefinite Feasibility Problems [article]

Hui Li, Chunhua Shen, Anton van den Hengel, Qinfeng Shi
2014 arXiv   pre-print
The computational complexity for an SDP with m constraints and matrices of size d by d is roughly reduced from O(m^3+md^3+m^2d^2) to O(d^3) (m>d in our case).  ...  In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA).  ...  The authors are with School of Computer Science, The University of Adelaide, Australia. C. Shen and A. van den Hengel are also with Australian Centre for Robotic Vision.  ... 
arXiv:1411.7450v1 fatcat:2gnyqk3gyncgzodeqfqfhzwwpm

A Semidefinite Relaxation Method for Elliptical Location

Xin Wang, Ying Ding, Le Yang
2020 Electronics  
We recognize that the root of these drawbacks lies in an oversimplified linear approximation of the nonconvex model, and accordingly design a maximum likelihood estimator through semidefinite relaxation  ...  Specifically, the design and implementation of position estimators are of great significance.  ...  The worst-case Newton complexity of an interior-point primal-dual path-following method is O(1)n 1 2 ln 1 .  ... 
doi:10.3390/electronics9010128 fatcat:lzjp2472zbe55aktlohez6qw7m

Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project [article]

Raphaël Bulle
2022 arXiv   pre-print
We provide comparisons with various other used estimators. An open-source implementation based on the FEniCS Project finite element software is provided as supplementary material.  ...  In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced.  ...  Roland Becker for the motivating and fruitful discussions.  ... 
arXiv:2102.04360v2 fatcat:o7654kvddffclcl2ihhnauaqny

Quasi-Newton Methods: A New Direction [article]

Philipp Hennig, Martin Kiefel (MPI for Intelligent Systems)
2012 arXiv   pre-print
Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function.  ...  This new notion elucidates some shortcomings of classical algorithms, and lights the way to a novel nonparametric quasi-Newton method, which is able to make more efficient use of available information  ...  Acknowledgments The authors thank Christian Schuler, Tom Minka and Carl Rasmussen for helpful discussions, as well as Carl Rasmussen for his release of minimize.m, which simplified development.  ... 
arXiv:1206.4602v1 fatcat:7egx6swimfdk3pzs6od5lozvci

A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits

Yunong Zhang, Jun Wang, Youshen Xia
2003 IEEE Transactions on Neural Networks  
Compared to other recurrent neural networks, the dual neural network is piecewise linear and has much simpler architecture with only one layer of neurons.  ...  Physical constraints such as joint limits and joint velocity limits, together with the drift-free criterion as a secondary task, are incorporated into the problem formulation of redundancy resolution.  ...  In the finite-time path-following task, the worst case of and , can be estimated on average as and , respectively, where , depends on the capacitive parameter .  ... 
doi:10.1109/tnn.2003.810607 pmid:18238046 fatcat:7xgb5daombb2ficqaovcjn4xie

A semi-definite programming approach for robust tracking

Shimrit Shtern, Aharon Ben-Tal
2015 Mathematical programming  
For such cases, robust estimation approaches, such as H ∞ filtering and set-value estimation, were introduced with the aim of providing filters with guaranteed worst case performance.  ...  The framework is extended to include the case of partially statistical noise, thus combining the KF and SVE frameworks.  ...  Therefore, we will now consider an alternative problem of computing the worst case estimation error based on the entire noise history.  ... 
doi:10.1007/s10107-015-0910-5 fatcat:p7opmf2fibaqbhq75b2bje5a5y

Efficient and Modular Implicit Differentiation [article]

Mathieu Blondel, Quentin Berthet, Marco Cuturi, Roy Frostig, Stephan Hoyer, Felipe Llinares-López, Fabian Pedregosa, Jean-Philippe Vert
2022 arXiv   pre-print
However, so far, implicit differentiation remained difficult to use for practitioners, as it often required case-by-case tedious mathematical derivations and implementations.  ...  In this paper, we propose automatic implicit differentiation, an efficient and modular approach for implicit differentiation of optimization problems.  ...  By running gradient descent for t iterations, we obtain an estimate x of x (θ) and an estimate J(x, θ) of ∂x (θ); cf. Definition 1.  ... 
arXiv:2105.15183v4 fatcat:dc3rq2nplvcmpjtkto44sej3r4

New Designs on MVDR Robust Adaptive Beamforming Based on Optimal Steering Vector Estimation [article]

Yongwei Huang, Mingkang Zhou, Sergiy A. Vorobyov
2018 arXiv   pre-print
In this case, the optimal beamformer is obtained by computing the sample matrix inverse and an optimal estimate of the signal of interest steering vector.  ...  The results are generalized to the case where an ellipsoidal constraint is considered, and sufficient conditions for the global optimality are derived.  ...  With respect of the estimate , the worst-case approach results in the diagonal loading of the data covariance matrix sample estimate.  ... 
arXiv:1810.11360v1 fatcat:xenefv2twvcyjcudnv3xt3vaqe

Rate analysis of inexact dual first order methods: Application to distributed MPC for network systems [article]

Ion Necoara, Valentin Nedelcu
2013 arXiv   pre-print
In particular, we provide, for the first time, estimates on the primal feasibility violation and primal and dual suboptimality of the generated approximate primal and dual solutions.  ...  In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems.  ...  Thus, for quadratic problems the worst case complexity per iteration of our method is O(n 2 ).  ... 
arXiv:1302.3129v1 fatcat:j3ftqzpzwfeazd6mm3jvvjpxku

Analysis and Design of Jump Coefficients in Discrete Stochastic Diffusion Models

Lina Meinecke, Stefan Engblom, Andreas Hellander, Per Lötstedt
2016 SIAM Journal on Scientific Computing  
The theory is tested in numerical experiments indicating that the new method is superior and minimizes also the forward error.  ...  The forward error, the error between the analytical solutions to the original and the perturbed equations, is bounded by the backward error, the error between the diffusion of the two equations.  ...  This work has been supported by the Swedish Research Council with grant number 621-2011-3148, the UPMARC Linnaeus center of Excellence, the Swedish strategic research programme eSSENCE, and the NIH grant  ... 
doi:10.1137/15m101110x pmid:28611531 pmcid:PMC5466879 fatcat:bcvo3ya7o5esrns3s5gbbnsiia

Power System Nonlinear State Estimation Using Distributed Semidefinite Programming

Hao Zhu, Georgios B. Giannakis
2014 IEEE Journal on Selected Topics in Signal Processing  
State estimation (SE) is an important task allowing power networks to monitor accurately the underlying system state, which is useful for security-constrained dispatch and power system control.  ...  Numerical tests on the standard IEEE 30-and 118-bus systems corroborate that the SE algorithms outperform existing alternatives, and approach near-optimal performance.  ...  TABLE II ESTIMATION II ERROR WITH OF CONVERGENCE FOR TEST CASE 2 TABLE III AVERAGE III RUNNING TIMES IN SECONDS TABLE IV ESTIMATION IV ERROR WITH OF CONVERGENCE FOR TEST CASE 3 For distribution  ... 
doi:10.1109/jstsp.2014.2331033 fatcat:6fx4c6ke5ray5ddsszvajsl75m

Robust Multicast Beamforming for Spectrum Sharing-Based Cognitive Radios

Yongwei Huang, Qiang Li, Wing-Kin Ma, Shuzhong Zhang
2012 IEEE Transactions on Signal Processing  
The problem is a nonconvex quadratically constrained quadratic program (QCQP), and in general it is hard to achieve the global optimality.  ...  Simulation results are presented to demonstrate the performance gains of the proposed algorithms over an existing robust design.  ...  ∥Δ ′ ∥ ≤ ′ ∥( + Δ ′ ) ∥ 2 ≤ , ∀ , (2c) where and ′ specify the bounds, or the worst-case magnitudes, of the CSI errors Δ and Δ ′ , respectively.  ... 
doi:10.1109/tsp.2011.2169061 fatcat:ymut5bjmqnbbhlon4n5apvutze
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