On Scaling Newton’s Method for Polar Decomposition and the Matrix Sign Function

1992 ◽  
Vol 13 (3) ◽  
pp. 688-706 ◽  
Author(s):  
Charles Kenney ◽  
Alan J. Laub
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Polar Decomposition ◽  
Matrix Sign Function ◽  
Sign Function ◽  
The Matrix

scholarly journals A Novel Iterative Method for Polar Decomposition and Matrix Sign Function

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
F. Soleymani ◽  
Predrag S. Stanimirović ◽  
Igor Stojanović
Keyword(s):  
Computational Complexity ◽  
Iterative Method ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Polar Decomposition ◽  
Matrix Sign Function ◽  
Sign Function ◽  
Globally Convergent ◽  
The Matrix ◽  
Analysis Of Stability

We define and investigate a globally convergent iterative method possessing sixth order of convergence which is intended to calculate the polar decomposition and the matrix sign function. Some analysis of stability and computational complexity are brought forward. The behaviors of the proposed algorithms are illustrated by numerical experiments.

The matrix sign function

1995 ◽  
Vol 40 (8) ◽  
pp. 1330-1348 ◽  
Author(s):  
C.S. Kenney ◽  
A.J. Laub
Keyword(s):  
Matrix Sign Function ◽  
Sign Function ◽  
The Matrix

scholarly journals Approximating the Matrix Sign Function Using a Novel Iterative Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
F. Soleymani ◽  
P. S. Stanimirović ◽  
S. Shateyi ◽  
F. Khaksar Haghani
Keyword(s):  
Iterative Method ◽  
Asymptotical Stability ◽  
Complex Matrix ◽  
Initial Matrix ◽  
Matrix Sign Function ◽  
Sign Function ◽  
The Matrix ◽  
Square Complex

This study presents a matrix iterative method for finding the sign of a square complex matrix. It is shown that the sequence of iterates converges to the sign and has asymptotical stability, provided that the initial matrix is appropriately chosen. Some illustrations are presented to support the theory.

scholarly journals A Geometric Newton Method for Oja's Vector Field

2009 ◽  
Vol 21 (5) ◽  
pp. 1415-1433 ◽  
Author(s):  
P.-A. Absil ◽  
M. Ishteva ◽  
L. De Lathauwer ◽  
S. Van Huffel
Keyword(s):  
Vector Field ◽  
Newton Method ◽  
Newton’S Method ◽  
Matrix Equation ◽  
Orthogonal Group ◽  
Newton's Method ◽  
Newton Algorithm ◽  
The Matrix ◽  
Geometric Techniques ◽  
The Way

Newton's method for solving the matrix equation [Formula: see text] runs up against the fact that its zeros are not isolated. This is due to a symmetry of F by the action of the orthogonal group. We show how differential-geometric techniques can be exploited to remove this symmetry and obtain a “geometric” Newton algorithm that finds the zeros of F. The geometric Newton method does not suffer from the degeneracy issue that stands in the way of the original Newton method.

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