scholarly journals Newton's method with exact line search for the square root of a matrix

2008 ◽  
Vol 96 ◽  
pp. 012034 ◽  
Author(s):  
J-h Long ◽  
X-y Hu ◽  
L Zhang
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Line Search ◽  
Square Root ◽  
Exact Line Search

Solving algebraic Riccati equations on parallel computers using Newton's method with exact line search

2000 ◽  
Vol 26 (10) ◽  
pp. 1345-1368 ◽  
Author(s):  
Peter Benner ◽  
Ralph Byers ◽  
Enrique S Quintana-Ortı́ ◽  
Gregorio Quintana-Ortı́
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Line Search ◽  
Riccati Equations ◽  
Parallel Computers ◽  
Algebraic Riccati Equations ◽  
Exact Line Search

scholarly journals A note on machine method for root extraction

2022 ◽  
Vol 40 ◽  
pp. 1-6
Author(s):  
Saroj Kumar Padhan ◽  
S. Gadtia
Keyword(s):  
Real Number ◽  
Newton’S Method ◽  
Newton's Method ◽  
Extraction Methods ◽  
Critical Study ◽  
Square Root ◽  
Machine Method ◽  
Iteration Formula ◽  
Root Extraction

The present investigation deals with the critical study of the works of Lancaster and Traub, who have developed $n$th root extraction methods of a real number. It is found that their developed methods are equivalent and the particular cases of Halley's and Householder's methods. Again the methods presented by them are easily obtained from simple modifications of Newton's method, which is the extension of Heron's square root iteration formula. Further, the rate of convergency of their reported methods are studied.

Newton’s method for solving the tensor square root problem

2019 ◽  
Vol 98 ◽  
pp. 57-62 ◽  
Author(s):  
Xue-Feng Duan ◽  
Cun-Yun Wang ◽  
Chun-Mei Li
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Square Root ◽  
Tensor Square

scholarly journals Newton’s Method for the Matrix Nonsingular Square Root

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chun-Mei Li ◽  
Shu-Qian Shen
Keyword(s):  
Stability Analysis ◽  
Newton’S Method ◽  
Newton's Method ◽  
Numerical Results ◽  
Square Root ◽  
Convergence Theorems ◽  
The Matrix ◽  
New Algorithms

Two new algorithms are proposed to compute the nonsingular square root of a matrixA. Convergence theorems and stability analysis for these new algorithms are given. Numerical results show that these new algorithms are feasible and effective.

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