The Quasi-Cauchy Relation and Diagonal Updating

1999 ◽  
Vol 9 (4) ◽  
pp. 1192-1204 ◽  
Author(s):  
M. Zhu ◽  
J. L. Nazareth ◽  
H. Wolkowicz
Keyword(s):  
Cauchy Relation ◽  
Diagonal Updating

scholarly journals An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammed Yusuf Waziri ◽  
Zanariah Abdul Majid
Keyword(s):  
Nonlinear Equations ◽  
Large Scale ◽  
Systems Of Nonlinear Equations ◽  
Numerical Comparison ◽  
Large Scale Systems ◽  
Additional Information ◽  
Cauchy Relation ◽  
Diagonal Updating ◽  
Quasi Newton

We present a new diagonal quasi-Newton update with an improved diagonal Jacobian approximation for solving large-scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi-Cauchy condition. The anticipation has been to further improve the performance of diagonal updating, by modifying the quasi-Cauchy relation so as to carry some additional information from the functions. The effectiveness of our proposed scheme is appraised through numerical comparison with some well-known Newton-like methods.

Refractive Index of Molten Li NO3– KNO2 and NaNO3 - NaNO2 Systems

1985 ◽  
Vol 40 (12) ◽  
pp. 1228-1230
Author(s):  
Y. Iwadate ◽  
J. Tominaga ◽  
K. Igarashi ◽  
J. Mochinaga
Keyword(s):  
Refractive Index ◽  
Electronic Polarization ◽  
Index Data ◽  
Cauchy Relation

Goniometry was used to measure the refractive indexes of molten LiNO3-KNO2 and NaNO3-NaNO2 mixtures.The index data were smoothed as functions of temperature and wavelength using the modified Cauchy relation. Information on electronic polarization is also reported.

Failure of the cauchy relation in cubic metals

1971 ◽  
Vol 5 (9) ◽  
pp. 787-790 ◽  
Author(s):  
J.F. Thomas
Keyword(s):  
Cubic Metals ◽  
Cauchy Relation

scholarly journals Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Mahboubeh Farid ◽  
Wah June Leong ◽  
Najmeh Malekmohammadi ◽  
Mustafa Mamat
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Hessian Matrix ◽  
Main Idea ◽  
Numerical Comparison ◽  
Rapid Control ◽  
Diagonal Approximation ◽  
Gradient Type ◽  
Diagonal Updating ◽  
Large Scale Unconstrained Optimization

We present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of identity matrix in the BB method. The main idea is to design a new diagonal updating scheme that incorporates scaling to instantly reduce the large eigenvalues of diagonal approximation and otherwise employs extra updates to increase small eigenvalues. These approaches give us a rapid control in the eigenvalues of the updating matrix and thus improve stepwise convergence. We show that our method is globally convergent. The effectiveness of the method is evaluated by means of numerical comparison with the BB method and its variant.

The generalized Cauchy relation as an universal property of the amorphous state

2005 ◽  
Vol 129 ◽  
pp. 45-49 ◽  
Author(s):  
J. K. Krüger ◽  
U. Müller ◽  
R. Bactavatchalou ◽  
J. Mainka ◽  
Ch. Gilow ◽  
...  
Keyword(s):  
Amorphous State ◽  
Universal Property ◽  
Cauchy Relation

scholarly journals Different glassy states, as indicated by a violation of the generalized Cauchy relation

2003 ◽  
Vol 5 ◽  
pp. 80-80 ◽  
Author(s):  
J K Kr ger ◽  
T Britz ◽  
A le Coutre ◽  
J Baller ◽  
W Possart ◽  
...  
Keyword(s):  
Cauchy Relation

scholarly journals Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Mahboubeh Farid ◽  
Wah June Leong ◽  
Lihong Zheng
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Positive Definite ◽  
Numerical Results ◽  
Type Method ◽  
Variable Space ◽  
Secant Equation ◽  
Gradient Type ◽  
Diagonal Updating ◽  
Large Scale Unconstrained Optimization

This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is justO(n). Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods.

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