A Preconditioned Iteration Method for Solving Sylvester Equations

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

A gradient based iterative solutions for Sylvester tensor equations

This paper is concerned with the numerical solution of the Sylvester tensor equation, which includes the Sylvester matrix equation as special case. By applying hierarchical identification principle proposed by Ding and Chen, 2005, and by using tensor arithmetic concepts, an iterative algorithm and its modification are established to solve the Sylvester tensor equation. Convergence analysis indicates that the iterative solutions always converge to the exact solution for arbitrary initial value. Finally, some examples are provided to show that the proposed algorithms are effective

A Gradient Based Iterative Solutions for Sylvester Tensor Equations

This paper is concerned with the numerical solution of the Sylvester tensor equation, which includes the Sylvester matrix equation as special case. By applying hierarchical identification principle proposed by Ding and Chen, 2005, and by using tensor arithmetic concepts, an iterative algorithm and its modification are established to solve the Sylvester tensor equation. Convergence analysis indicates that the iterative solutions always converge to the exact solution for arbitrary initial value. Finally, some examples are provided to show that the proposed algorithms are effective

Gradient Based Iterative Algorithm to Solve General Coupled Discrete-Time Periodic Matrix Equations over Generalized Reflexive Matrices

The discrete-time periodic matrix equations are encountered in periodic state feedback problems and model reduction of periodic descriptor systems. The aim of this paper is to compute the generalized reflexive solutions of the general coupled discrete-time periodic matrix equations. We introduce a gradient-based iterative (GI) algorithm for finding the generalized reflexive solutions of the general coupled discretetime periodic matrix equations. It is shown that the introduced GI algorithm always converges to the generalized reflexive solutions for any initial generalized reflexive matrices. Finally, two numerical examples are investigated to confirm the efficiency of GI algorithm

Calibration of spatial relationships between multiple robots and sensors

Classic hand-eye calibration methods have been limited to single robots and sensors. Recently a new calibration formulation for multiple robots has been proposed that solves for the extrinsic calibration parameters for each robot simultaneously instead of sequentially. The existing solutions for this new problem required data to have correspondence, but Ma, Goh and Chirikjian (MGC) proposed a probabilistic method to solve this problem which eliminated the need for correspondence. In this thesis, the literature of the various robot-sensor calibration problems and solutions are surveyed, and the MGC method is reviewed in detail. Lastly comparison with other methods using numerical simulations were carried out to draw some conclusions

Open Systems, Entanglement and Quantum Optics

The subject of this book is a presentation of some aspects of modern theory of open quantum systems. It introduces several up-to- date topics, such as detecting quantum entanglement, modeling of quantum noise, quantum communication processes, and computational complexity in the analysis of quantum operations. Also discussed are light propagation in optically dressed media, as well as entropy and information measure for quantized electromagnetic fields media. This book is intended for researchers and students interested in the theory of open quantum systems, quantum information theory and quantum systems interacting with electromagnetic fields