Results 71 to 80 of about 281 (133)
Extended block Hessenberg method for large-scale Sylvester differential matrix equations [PDF]
Journal of Mahani Mathematical ResearchIn this paper, we consider large-scale low-rank Sylvester differential matrix equations. We present two iterative methods for the approximate solution of such differential matrix equations. In the first method, exploiting the extended block Krylov method,
Azita Tajaddini
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Toward Krylov-based holography in double-scaled SYK
Journal of High Energy PhysicsBuilding on the duality between Krylov complexity and geodesic length in Jackiw-Teitelboim and sine-dilaton gravity, we develop a precise holographic dictionary for quantities in the Krylov subspace of the double-scaled Sachdev-Ye-Kitaev model (DSSYK ...
Yichao Fu +3 more
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Developing Hessian–Free Second–Order Adversarial Examples for Adversarial Training
International Journal of Applied Mathematics and Computer ScienceRecent studies show that deep neural networks (DNNs) are extremely vulnerable to elaborately designed adversarial examples. Adversarial training, which uses adversarial examples as training data, has been proven to be one of the most effective methods of
Qian Yaguan +5 more
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Krylov complexity in the Schrödinger field theory
Journal of High Energy PhysicsWe investigate the Krylov complexity of Schrödinger field theories, focusing on both bosonic and fermionic systems within the grand canonical ensemble which includes a chemical potential.
Peng-Zhang He, Hai-Qing Zhang
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AlgorithmsGMRES is one of the most powerful and popular methods to solve linear systems in the Krylov subspace; we examine it from two viewpoints: to maximize the decreasing length of the residual vector, and to maintain the orthogonality of the consecutive ...
Chein-Shan Liu +2 more
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Stochastic estimation of level density in nuclear shell-model calculations
EPJ Web of Conferences, 2016 An estimation method of the nuclear level density stochastically based on nuclear shell-model calculations is introduced. In order to count the number of the eigen-values of the shell-model Hamiltonian matrix, we perform the contour integral of the ...
Shimizu Noritaka +5 more
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Blind adaptive Krylov subspace multiuser detection
IEEE 54th Vehicular Technology Conference. VTC Fall 2001. Proceedings (Cat. No.01CH37211), 2002 A new method for low-complexity Multiuser Detection (MUD)based in the Fast Subspace Decomposition (FSD) is proposed. The use of FSD allows the estimation of the number of users along with the multiuser detection on line. This leads to a fast multiuser estimation-detection scheme with ultra-low complexity.
Antonio J. Caamaño +2 more
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Krylov Subspace Descent for Deep Learning
, 2011 In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace formed by the gradient and an approximation to the Hessian matrix, and then use a subset of the training data ...
Oriol Vinyals, Daniel Povey
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A Global Krylov Subspace Method for the Sylvester Quaternion Matrix Equation
Journal of New TheoryThis study concerns the Sylvester matrix equation in the quaternion setting when the coefficient matrices as well as the unknown matrix have quaternion entries.
Sinem Şimşek
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Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems
Abstract and Applied Analysis, 2014 Based on the modified Hermitian and skew-Hermitian splitting (MHSS) and preconditioned MHSS (PMHSS) methods, a generalized preconditioned MHSS (GPMHSS) method for a class of complex symmetric linear systems is presented.
Cui-Xia Li, Yan-Jun Liang, Shi-Liang Wu
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