Continuity of the core-EP inverse and its applications

In this paper, firstly we study the continuity of the core-EP inverse without explicit error bounds by virtue of two methods. One is the rank equality, followed from the classical generalized inverse. The other one is matrix decomposition. The continuity of the core inverse can be derived as a particular case. Secondly, we study perturbation bounds for the core-EP inverse under prescribed conditions. Perturbation bounds for the core inverse can be derived as a particular case. Also, as corollaries, the sufficient (and necessary) conditions for the continuity of the core-EP inverse are obtained. Thirdly, a numerical example is illustrated to compare derived upper bounds. Finally, an application to semistable matrices is provided.This research is supported by the National Natural Science Foundation of China (No. 11771076), partially supported by FCT-'Fundacao para a Ciencia e a Tecnologia', within the project UID-MAT-00013/2013

Representations and properties of the W-weighted core-EP inverse

In this paper, we investigate the weighted core-EP inverse introduced by Ferreyra, Levis and Thome. Several computational representations of the weighted core-EP inverse are obtained in terms of singular-value decomposition, full-rank decomposition and QR decomposition. These representations are expressed in terms of various matrix powers as well as matrix product involving the core-EP inverse, Moore-Penrose inverse and usual matrix inverse. Finally, those representations involving only Moore-Penrose inverse are compared and analyzed via computational complexity and numerical examples.This research is supported by the National Natural Science Foundation of China (No.11771076), the Scientific Innovation Research of College Graduates in Jiangsu Province (No.KYZZ16 0112), Partially supported by FCT- ‘Fundação para a Ciência e a Tecnologia’, within the project UID-MAT-00013/2013

The pseudo core inverse of a companion matrix

The notion of core inverse was introduced by Baksalary and Trenkler for a complex matrix of index 1. Recently, the notion of pseudo core inverse extended the notion of core inverse to an element of an arbitrary index in *-rings; meanwhile, it characterized the core-EP inverse introduced by Manjunatha Prasad and Mohana for complex matrices, in terms of three equations. Many works have been done on classical generalized inverses of companion matrices and Toeplitz matrices. In this paper, we discuss existence criteria and formulae of the pseudo core inverse of a companion matrix over a *-ring. A {1, 3}-inverse of a Toeplitz matrix plays an important role in that process.- This research is supported by the National Natural Science Foundation of China (No.11771076, No.11471186), the Scientific Innovation Research of College Graduates in Jiangsu Province (No.KYZZ16_0112)

Stage-oriented Comprehensive Acupuncture Treatment plus Rehabilitation Training for Apoplectic Hemiplegia

ObjectiveTo study the effect of stage-oriented comprehensive acupuncture treatment plus rehabilitation training for the recovery of apoplectic hemiplegia.MethodsThe 60 cases of acute apoplectic hemiplegia were divided randomly into the treatment and control groups with 30 in each. Based on the routine medication, acupuncture combined with modern rehabilitation techniques was applied for the treatment group, while only rehabilitation treatment for the control group. Before and three months after treatment, the evaluation was done on the motor function and daily life ability for both groups respectively with simplified Fugl-Meyer Evaluation and modified Barthel index.ResultsThe therapeutic effect of treatment group was significantly superior to that of the control group (P<0.05).ConclusionsBased on Brunnstrom's theory of six-stage in the recovery of hemiplegia, the effect of stage-oriented comprehensive acupuncture therapy combined with rehabilitation training is very good, helpful in raising the daily life ability of patients

Tensor Factor Model Estimation by Iterative Projection

Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to Tucker tensor decomposition, except that the time dimension is treated as a dynamic process with a time dependent structure. In this paper we introduce two approaches to estimate such a tensor factor model by using iterative orthogonal projections of the original tensor time series. The approaches extend the existing estimation procedures and our theoretical investigation shows that they improve the estimation accuracy and convergence rate significantly. The developed approaches are similar to higher order orthogonal projection methods for tensor decomposition, but with significant differences and theoretical properties. Simulation study is conducted to further illustrate the statistical properties of these estimators