scholarly journals A Newton’s iteration converges quadratically to nonisolated solutions too

2021 ◽  
pp. 1
Author(s):  
Zhonggang Zeng
Keyword(s):  
Newton's Iteration

scholarly journals A Preconditioned Iteration Method for Solving Sylvester Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jituan Zhou ◽  
Ruirui Wang ◽  
Qiang Niu
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Newton's Iteration ◽  
Gradient Based ◽  
Selection Of

A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method.

Computing the Number of Fixed Joints on Poincare Map in Nonlinear Mathieu Equation

1993 ◽  
Author(s):  
Hisato Fujisaka ◽  
Chikara Sato
Keyword(s):  
Differential Equations ◽  
Fixed Points ◽  
Numerical Method ◽  
Topological Degree ◽  
Poincaré Map ◽  
Mathieu Equation ◽  
Time Varying ◽  
Poincare Map ◽  
Newton's Iteration ◽  
Combined Use

Abstract A numerical method is presented to compute the number of fixed points of Poincare maps in ordinary differential equations including time varying equations. The method’s fundamental is to construct a map whose topological degree equals to the number of fixed points of a Poincare map on a given domain of Poincare section. Consequently, the computation procedure is simply computing the topological degree of the map. The combined use of this method and Newton’s iteration gives the locations of all the fixed points in the domain.

7. Newton's Iteration for Structured Matrices

1999 ◽  
pp. 189-210 ◽  
Author(s):  
Victor Y. Pan ◽  
Sheryl Branham ◽  
Rhys E. Rosholt ◽  
Ai-Long Zheng
Keyword(s):  
Structured Matrices ◽  
Newton's Iteration

scholarly journals A Fast Newton's Iteration for M/G/1-Type and GI/M/1-Type Markov Chains

2012 ◽  
Vol 28 (4) ◽  
pp. 557-583 ◽  
Author(s):  
Juan F. Pérez ◽  
Miklós Telek ◽  
Benny Van Houdt
Keyword(s):  
Markov Chains ◽  
Newton's Iteration
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