scholarly journals The Steepest Descent Method for Orthogonal Polynomials on the Real Line with Varying Weights

2008 ◽  
Vol 2008 ◽  
Author(s):  
K. T.-R. McLaughlin ◽  
P. D. Miller
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
The Real

scholarly journals Sylvester equations for Laguerre–Hahn orthogonal polynomials on the real line

2013 ◽  
Vol 219 (17) ◽  
pp. 9118-9131 ◽  
Author(s):  
A. Branquinho ◽  
A. Paiva ◽  
M.N. Rebocho
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
The Real

scholarly journals A Learning Method for Neural Networks Based on a Pseudoinverse Technique

1996 ◽  
Vol 3 (3) ◽  
pp. 201-209 ◽  
Author(s):  
Chinmoy Pal ◽  
Ichiro Hagiwara ◽  
Naoki Kayaba ◽  
Shin Morishita
Keyword(s):  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Learning Method ◽  
Theoretical Formulation ◽  
Learning Capability ◽  
Fast Learning ◽  
Backpropagation Method ◽  
Mass Spring ◽  
Exclusive Or

A theoretical formulation of a fast learning method based on a pseudoinverse technique is presented. The efficiency and robustness of the method are verified with the help of an Exclusive OR problem and a dynamic system identification of a linear single degree of freedom mass–spring problem. It is observed that, compared with the conventional backpropagation method, the proposed method has a better convergence rate and a higher degree of learning accuracy with a lower equivalent learning coefficient. It is also found that unlike the steepest descent method, the learning capability of which is dependent on the value of the learning coefficient ν, the proposed pseudoinverse based backpropagation algorithm is comparatively robust with respect to its equivalent variable learning coefficient. A combination of the pseudoinverse method and the steepest descent method is proposed for a faster, more accurate learning capability.

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