On inhomogeneous Diophantine approximation and the Borweins’ algorithm. II - Komatsu - 1999 () Citation Context ... a comprehensive list of references. In the last decade, interest in these problems was rekind
最后，介绍了负梯度算法在深度学习中的应用。 关键词 Barzilai-Borwein 型算法，负梯度算法，初始步长，算法的应用 Discussion on Barzilai-Borwein Algorithm Ya’nan Huang School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha Hunan Received: Mar. 26th , 2022; accepted:...
general objective unctions. Numerical experiments show that our algorithms are more efective when compared with some existing conjugate gradient methods. Key words: Barzilai-Borwein gradient method, quasi-Newton equation, BF- GS method, adaptive regularization algorithm with cubics, conjugate gradient metho...
To adapt the algorithm for solving saddle point problems, we also extend the R -linear convergence result to the case when the right-hand term k is replaced by k -1. Although our theoretical analyses cannot provide a good estimate to the parameter , in practice, we find that can be as ...
S. Ghadimi et al. Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization I: a generic algorithmic framework SIAM J. Optim. (2012) D. Needell et al. Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm Proceedings of the Advances...
Then, after selecting the default value of the momentum factor, we tested the algorithm’s robustness using different initial learning rates and parameters. Finally, we conducted comparative experiments on the four improved algorithms to analyze the effects Experimental result In this section, we will...
The Barzilai and Borwein gradient method does not ensure descent in the objective function at each iteration, but performs better than the classical steepest descent method in practical computations. Combined with the technique of nonmonotone line search etc., such a method has found successful applica...
proved to be a symmetric block-Toeplitz-Toeplitz-block matrix (BTTB). Next ，assuming that the coefficient matrix is positive definite ，the BB method is used to solve the equations of downward continuation ，and the iterative step is limited to ensure the convergence of the algorithm. ...
AnindispensabletoolforexperimentalmathematicsisFerguson’sPSLQalgorithm,used, forexample,byDavidBailey,Jon’sbrotherPeterBorweinandSimonPlouffe(Bailey, Borwein,&Plouffe,1997)todiscovertheformulanowknownasBBP-formula: π¼ X ∞ i¼0 1 16 i 4 8iþ1 − 2 8iþ4 − 1 8iþ5 − 1 8iþ...
Bailey, DH (1988) The Computation of a to 29.360.000 decimal digits using Borweins quartically convergent algorithm. Math. Comput. 50: pp. 283-96Bailey, D. H., \The Computation of to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm", preprint....