scholarly journals A New Version of the Accelerated Overrelaxation Iterative Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Shi-Liang Wu ◽  
Yu-Jun Liu
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
Positive Definite ◽  
System Of Linear Equations ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Convergence Results ◽  
Aor Method ◽  
Symmetric Positive Definite Matrices ◽  
Overrelaxation Iterative Method

Hadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant,L-matrices, and consistently orders matrices. In this paper, a new version of the AOR method is presented. Some convergence results are derived when the coefficient matrices are irreducible diagonal dominant,H-matrices, symmetric positive definite matrices, andL-matrices. A relational graph for the new AOR method and the original AOR method is presented. Finally, a numerical example is presented to illustrate the efficiency of the proposed method.

A Trace Inequality for Symmetric Nonnegative Definite Matrices

2011 ◽  
Vol 225-226 ◽  
pp. 970-973
Author(s):  
Shi Qing Wang
Keyword(s):  
Control Theory ◽  
Communication Systems ◽  
Positive Definite ◽  
Trace Inequality ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Multiple Input ◽  
Nonnegative Definite ◽  
Symmetric Positive Definite Matrices ◽  
Trace Inequalities

Trace inequalities naturally arise in control theory and in communication systems with multiple input and multiple output. One application of Belmega’s trace inequality has already been identified [3]. In this paper, we extend the symmetric positive definite matrices of his inequality to symmetric nonnegative definite matrices, and the inverse matrices to Penrose-Moore inverse matrices.

scholarly journals EEG representation using multi-instance framework on the manifold of symmetric positive definite matrices

2019 ◽  
Vol 16 (3) ◽  
pp. 036016 ◽  
Author(s):  
Khadijeh Sadatnejad ◽  
Mohammad Rahmati ◽  
Reza Rostami ◽  
Reza Kazemi ◽  
Saeed S Ghidary ◽  
...  
Keyword(s):  
Positive Definite ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Symmetric Positive Definite Matrices

scholarly journals A GPU solver for symmetric positive-definite matrices vs. traditional codes

2019 ◽  
Vol 78 (9) ◽  
pp. 2933-2943 ◽  
Author(s):  
Jan Bohacek ◽  
Abdellah Kharicha ◽  
Andreas Ludwig ◽  
Menghuai Wu ◽  
Tobias Holzmann ◽  
...  
Keyword(s):  
Positive Definite ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Symmetric Positive Definite Matrices

scholarly journals Geometry-aware manipulability learning, tracking, and transfer

2020 ◽  
pp. 027836492094681
Author(s):  
Noémie Jaquier ◽  
Leonel Rozo ◽  
Darwin G Caldwell ◽  
Sylvain Calinon
Keyword(s):  
Gaussian Mixture ◽  
Positive Definite ◽  
Robotic Hand ◽  
Redundant Manipulators ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Task Requirements ◽  
Robot Performance ◽  
Symmetric Positive Definite Matrices ◽  
Dual Arm

Body posture influences human and robot performance in manipulation tasks, as appropriate poses facilitate motion or the exertion of force along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze, control, and design the robot dexterity as a function of the articulatory joint configuration. This descriptor can be designed according to different task requirements, such as tracking a desired position or applying a specific force. In this context, this article presents a novel manipulability transfer framework, a method that allows robots to learn and reproduce manipulability ellipsoids from expert demonstrations. The proposed learning scheme is built on a tensor-based formulation of a Gaussian mixture model that takes into account that manipulability ellipsoids lie on the manifold of symmetric positive-definite matrices. Learning is coupled with a geometry-aware tracking controller allowing robots to follow a desired profile of manipulability ellipsoids. Extensive evaluations in simulation with redundant manipulators, a robotic hand and humanoids agents, as well as an experiment with two real dual-arm systems validate the feasibility of the approach.

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