Convergence of density functional iterative procedures with a Newton-Raphson algorithm

2007 ◽  
Vol 6 (1-3) ◽  
pp. 349-352 ◽  
Author(s):  
J. W. Jerome ◽  
P. R. Sievert ◽  
L. H. Ye ◽  
I. G. Kim ◽  
A. J. Freeman
Keyword(s):  
Density Functional ◽  
Newton Raphson ◽  
Iterative Procedures ◽  
Raphson Algorithm

A Class of Decision Processes Showing Policy-Improvement/Newton–Raphson Equivalence

1989 ◽  
Vol 3 (3) ◽  
pp. 397-403 ◽  
Author(s):  
P. Whittle
Keyword(s):  
Optimality Condition ◽  
Regularity Condition ◽  
Decision Processes ◽  
Policy Improvement ◽  
Improvement Algorithm ◽  
Newton Raphson ◽  
Raphson Algorithm

A condition expressed in Eq. (7) is given which, with one simplifying regularity condition, ensures that the policy-improvement algorithm is equivalent to application of the Newton–Raphson algorithm to an optimality condition. It is shown that this condition covers the two known cases of such equivalence, and another example is noted. The condition is believed to be necessary to within transformations of the problem, but this has not been proved.

scholarly journals An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

2013 ◽  
Vol 23 (1) ◽  
pp. 117-129 ◽  
Author(s):  
Jiawen Bian ◽  
Huiming Peng ◽  
Jing Xing ◽  
Zhihui Liu ◽  
Hongwei Li
Keyword(s):  
Parameter Estimation ◽  
Convergence Rate ◽  
Efficient Algorithm ◽  
Numerical Experiments ◽  
Additive Noise ◽  
Mean Squared Errors ◽  
Least Squares Estimators ◽  
The Mean ◽  
Newton Raphson ◽  
Raphson Algorithm

This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton-Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton- Raphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators (LSEs) under the same noise conditions, but it outperforms LSEs in terms of the mean squared errors. Finally, the effectiveness of the algorithm is verified by some numerical experiments.

Generalized Newton–Raphson algorithm for high dimensional LASSO regression

2021 ◽  
Vol 14 (3) ◽  
pp. 339-350
Author(s):  
Yueyong Shi ◽  
Jian Huang ◽  
Yuling Jiao ◽  
Yicheng Kang ◽  
Hu Zhang
Keyword(s):  
High Dimensional ◽  
Lasso Regression ◽  
Newton Raphson ◽  
Generalized Newton ◽  
Raphson Algorithm

Double-Mode Energy Management for Multi-Energy System via Distributed Dynamic Event-Triggered Newton-Raphson Algorithm

2020 ◽  
Vol 11 (6) ◽  
pp. 5339-5356 ◽  
Author(s):  
Yushuai Li ◽  
David Wenzhong Gao ◽  
Wei Gao ◽  
Huaguang Zhang ◽  
Jianguo Zhou
Keyword(s):  
Energy Management ◽  
Energy System ◽  
Dynamic Event ◽  
Newton Raphson ◽  
Mode Energy ◽  
Event Triggered ◽  
Raphson Algorithm

scholarly journals Blended Root Finding Algorithm Outperforms Bisection and Regula Falsi Algorithms

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1118
Author(s):  
Sabharwal
Keyword(s):  
Computational Complexity ◽  
Empirical Evidence ◽  
Analytic Solution ◽  
Fundamental Problem ◽  
Numerical Techniques ◽  
Physical Sciences ◽  
Root Finding ◽  
Numerical Computing ◽  
Newton Raphson ◽  
Raphson Algorithm

Finding the roots of an equation is a fundamental problem in various fields, including numerical computing, social and physical sciences. Numerical techniques are used when an analytic solution is not available. There is not a single algorithm that works best for every function. We designed and implemented a new algorithm that is a dynamic blend of the bisection and regula falsi algorithms. The implementation results validate that the new algorithm outperforms both bisection and regula falsi algorithms. It is also observed that the new algorithm outperforms the secant algorithm and the Newton–Raphson algorithm because the new algorithm requires fewer computational iterations and is guaranteed to find a root. The theoretical and empirical evidence shows that the average computational complexity of the new algorithm is considerably less than that of the classical algorithms.

Policy Improvement and the Newton–Raphson Algorithm for Renewal Reward Processes

1989 ◽  
Vol 3 (3) ◽  
pp. 393-396 ◽  
Author(s):  
J. M. McNamara
Keyword(s):  
Continuous Time ◽  
Successive Approximations ◽  
Average Reward ◽  
Policy Improvement ◽  
Unique Root ◽  
Renewal Reward Processes ◽  
Reward Process ◽  
Newton Raphson ◽  
Renewal Reward Process ◽  
Raphson Algorithm

We consider a renewal reward process in continuous time. The supremum average reward, γ* for this process can be characterised as the unique root of a certain function. We show how one can apply the Newton–Raphson algorithm to obtain successive approximations to γ*, and show that the successive approximations so obtained are the same as those obtained by using the policy improvement technique.

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