Results 91 to 100 of about 3,994 (221)

Fast sampling from a Gaussian Markov random field using Krylov subspace approaches

, 2008
Many applications in spatial statistics, geostatistics and image analysis require efficient techniques for sampling from large Gaussian Markov random fields (GMRFs).
Simpson, Daniel P., Pettitt, Anthony N., Turner, Ian W.   +2 more
core  

Toward Krylov-based holography in double-scaled SYK

Journal of High Energy Physics
Building 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, Hyun-Sik Jeong, Keun-Young Kim, Juan F. Pedraza   +3 more
doaj   +1 more source

Developing Hessian–Free Second–Order Adversarial Examples for Adversarial Training

International Journal of Applied Mathematics and Computer Science
Recent 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, Zhang Liangjian, Wang Yuqi, Ji Boyuan, Yao Tengteng, Wang Bin   +5 more
doaj   +1 more source

Flexible Inner-Outer Krylov Subspace Methods

, 2002
Flexible Krylov methods refers to a class of methods which accept preconditioning that can change from one step to the next. Given a Krylov subspace method, such as CG, GMRES, QMR, etc. for the solution of a linear system Ax = b, instead of having a xed
B. Szyld, Daniel B. Szyld, Valeria Simoncini, Daniel   +3 more
core  

Communication-Avoiding Krylov Subspace Methods in Theory and Practice [PDF]

, 2015
Advancements in the field of high-performance scientific computing are necessary to address the most important challenges we face in the 21st century. From physical modeling to large-scale data analysis, engineering efficient code at the extreme scale ...
Carson, Erin Claire
core  

Krylov complexity in the Schrödinger field theory

Journal of High Energy Physics
We 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
doaj   +1 more source

A Global Krylov Subspace Method for the Sylvester Quaternion Matrix Equation

Journal of New Theory
This 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
doaj   +1 more source

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, Utsuno Yutaka, Futamura Yasunori, Sakurai Tetsuya, Mizusaki Takahiro, Otsuka Takaharu   +5 more
doaj   +1 more source

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
openaire   +3 more sources

Re-Orthogonalized/Affine GMRES and Orthogonalized Maximal Projection Algorithm for Solving Linear Systems

Algorithms
GMRES 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, Chih-Wen Chang , Chung-Lun Kuo    +2 more
doaj   +1 more source