Exploiting the connection between PLS, Lanczos methods and conjugate gradients: alternative proofs of some properties of PLS

2002 ◽  
Vol 16 (7) ◽  
pp. 361-367 ◽  
Author(s):  
Aloke Phatak ◽  
Frank de Hoog
Keyword(s):  
Conjugate Gradients ◽  
Lanczos Methods

scholarly journals Iterative Methods for the Computation of the Perron Vector of Adjacency Matrices

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1522
Author(s):  
Anna Concas ◽  
Lothar Reichel ◽  
Giuseppe Rodriguez ◽  
Yunzi Zhang
Keyword(s):  
Iterative Methods ◽  
Adjacency Matrix ◽  
Lanczos Method ◽  
Power Method ◽  
Arnoldi Method ◽  
Multiple Eigenvalues ◽  
Computer Storage ◽  
Adjacency Matrices ◽  
Lanczos Methods ◽  
Perron Vector

The power method is commonly applied to compute the Perron vector of large adjacency matrices. Blondel et al. [SIAM Rev. 46, 2004] investigated its performance when the adjacency matrix has multiple eigenvalues of the same magnitude. It is well known that the Lanczos method typically requires fewer iterations than the power method to determine eigenvectors with the desired accuracy. However, the Lanczos method demands more computer storage, which may make it impractical to apply to very large problems. The present paper adapts the analysis by Blondel et al. to the Lanczos and restarted Lanczos methods. The restarted methods are found to yield fast convergence and to require less computer storage than the Lanczos method. Computed examples illustrate the theory presented. Applications of the Arnoldi method are also discussed.

Parallel computation of arbitrarily shaped waveguide modes using BI-RME and Lanczos methods

2006 ◽  
Vol 23 (4) ◽  
pp. 273-284
Author(s):  
A. M. Vidal ◽  
A. Vidal ◽  
V. E. Boria ◽  
V. M. García
Keyword(s):  
Parallel Computation ◽  
Waveguide Modes ◽  
Lanczos Methods

ACCELERATING TRAINING OF FEEDFORWARD NEURAL NETWORKS

1994 ◽  
Vol 03 (03) ◽  
pp. 339-348
Author(s):  
CARL G. LOONEY
Keyword(s):  
Neural Networks ◽  
Local Minimum ◽  
Random Search ◽  
Feedforward Neural Networks ◽  
Conjugate Gradients ◽  
Activation Functions ◽  
Problematic Behavior ◽  
Methods And Techniques ◽  
Adaptive Step ◽  
Quality Learning

We review methods and techniques for training feedforward neural networks that avoid problematic behavior, accelerate the convergence, and verify the training. Adaptive step gain, bipolar activation functions, and conjugate gradients are powerful stabilizers. Random search techniques circumvent the local minimum trap and avoid specialization due to overtraining. Testing assures quality learning.

A matrix analysis of Arnoldi and Lanczos methods

1998 ◽  
Vol 81 (1) ◽  
pp. 125-141 ◽  
Author(s):  
V. Simoncini
Keyword(s):  
Matrix Analysis ◽  
Lanczos Methods

scholarly journals A Frame-Based Conjugate Gradients Direct Search Method with Radial Basis Function Interpolation Model

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaowei Fang ◽  
Qin Ni
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Direct Search ◽  
Search Method ◽  
Conjugate Gradients ◽  
Test Problems ◽  
Interpolation Model ◽  
Direct Search Method ◽  
Radial Basis Function Interpolation ◽  
Radial Basis

In this paper, we propose a new hybrid direct search method where a frame-based PRP conjugate gradients direct search algorithm is combined with radial basis function interpolation model. In addition, the rotational minimal positive basis is used to reduce the computation work at each iteration. Numerical results for solving the CUTEr test problems show that the proposed method is promising.

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