Rehabilitation training is believed to be an effectual strategy that canreduce the risk of dysfunction caused by spasticity.However,achieving visualizationrehabilitation training for patients remains clinically challe...Rehabilitation training is believed to be an effectual strategy that canreduce the risk of dysfunction caused by spasticity.However,achieving visualizationrehabilitation training for patients remains clinically challenging.Herein,wepropose visual rehabilitation training system including iontronic meta-fabrics withskin-friendly and large matrix features,as well as high-resolution image modules fordistribution of human muscle tension.Attributed to the dynamic connection and dissociationof the meta-fabric,the fabric exhibits outstanding tactile sensing properties,such as wide tactile sensing range(0~300 kPa)and high-resolution tactile perception(50 Pa or 0.058%).Meanwhile,thanks to the differential capillary effect,the meta-fabric exhibits a“hitting three birds with one stone”property(dryness wearing experience,long working time and cooling sensing).Based on this,the fabrics can be integrated with garmentsand advanced data analysis systems to manufacture a series of large matrix structure(40×40,1600 sensing units)training devices.Significantly,the tunability of piezo-ionic dynamics of the meta-fabric and the programmability of high-resolution imaging modules allowthis visualization training strategy extendable to various common disease monitoring.Therefore,we believe that our study overcomes theconstraint of standard spasticity rehabilitation training devices in terms of visual display and paves the way for future smart healthcare.展开更多
In 3D frequency domain seismic forward and inversion calculation,the huge amount of calculation and storage is one of the main factors that restrict the processing speed and calculation efficiency.The frequency domain...In 3D frequency domain seismic forward and inversion calculation,the huge amount of calculation and storage is one of the main factors that restrict the processing speed and calculation efficiency.The frequency domain finite-difference forward simulation algorithm based on the acoustic wave equation establishes a large bandwidth complex matrix according to the discretized acoustic wave equation,and then the frequency domain wave field value is obtained by solving the matrix equation.In this study,the predecessor's optimized five-point method is extended to a 3D seven-point finite-difference scheme,and then a perfectly matched layer absorbing boundary condition(PML)is added to establish the corresponding matrix equation.In order to solve the complex matrix,we transform it to the equivalent real number domain to expand the solvable range of the matrix,and establish two objective functions to transform the matrix solving problem into an optimization problem that can be solved using gradient methods,and then use conjugate gradient algorithm to solve the problem.Previous studies have shown that in the conjugate gradient algorithm,the product of the matrix and the vector is the main factor that affects the calculation efficiency.Therefore,this study proposes a method that transform bandwidth matrix and vector product problem into some equivalent vector and vector product algorithm,thereby reducing the amount of calculation and storage.展开更多
We recently performed a series of improvement on evaluation of eigenvalues without complicated iterations.In this work we first discuss evaluation of the lowest eigenvalue for given systems,by which one conveniently o...We recently performed a series of improvement on evaluation of eigenvalues without complicated iterations.In this work we first discuss evaluation of the lowest eigenvalue for given systems,by which one conveniently obtains the value of the lowest eigenvalue based on the dimension and width of given matrix.We also discuss a strong correlation between eigenvalues and diagonal matrix elements for large matrices,by which one is able to predict eigenvalues approximately without iterations.展开更多
The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, ...The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, it is shown in this paper that under the original given condition the inexact RQI may not quadratically converge to the desired eigenpair and even may misconverge to some other undesired eigenpair. A new condition, called the uniform positiveness condition, is given that can fix misconvergence problem and ensure the quadratic convergence of the inexact RQI. An alternative to the inexact RQI is the Jacobi-Davidson (JD) method without subspace acceleration. A new proof of its linear convergence is presented and a sharper bound is established in the paper. All the results are verified and analyzed by numerical experiments.展开更多
As is well known, solving matrix multiple eigenvalue problems is a very difficult topic. In this paper, Arnoldi type algorithms are proposed for large unsymmetric multiple eigenvalue problems when the matrix A involve...As is well known, solving matrix multiple eigenvalue problems is a very difficult topic. In this paper, Arnoldi type algorithms are proposed for large unsymmetric multiple eigenvalue problems when the matrix A involved is diagonalizable. The theoretical background is established, in which lower and upper error bounds for eigenvectors are new for both Arnoldi's method and a general perturbation problem, and furthermore these bounds are shown to be optimal and they generalize a classical perturbation bound due to W. Kahan in 1967 for A symmetric. The algorithms can adaptively determine the multiplicity of an eigenvalue and a basis of the associated eigenspace. Numerical experiments show reliability of the algorithms.展开更多
基金supported by the National Key Research and Development Program(2022YFB3805800)National Natural Science Foundation of China(52473307,22208178,62301290)+9 种基金Taishan Scholar Program of Shandong Province in China(tsqn202211116)Shandong Provincial Universities Youth Innovation Technology Plan Team(2023KJ223)Natural Science Foundation of Shandong Province of China(ZR2023YQ037,ZR2020QE074,ZR2023QE043,ZR2022QE174)Shandong Province Science and Technology Small and Medium sized Enterprise Innovation Ability Enhancement Project(2023TSGC0344,2023TSGC1006)Natural Science Foundation of Qingdao(23-2-1-249-zyyd-jch,24-4-4-zrjj-56-jch)Anhui Province Postdoctoral Researcher Research Activity Funding Project(2023B706)Qingdao Key Technology Research and Industrialization Demonstration Projects(23-1-7-zdfn-2-hz)Qingdao Shinan District Science and Technology Plan Project(2022-3-005-DZ)Suqian Key Research and Development Plan(H202310)Jinan City-School Integration Development Strategy Project for the Year 2023 under Grant(JNSX2023088).
文摘Rehabilitation training is believed to be an effectual strategy that canreduce the risk of dysfunction caused by spasticity.However,achieving visualizationrehabilitation training for patients remains clinically challenging.Herein,wepropose visual rehabilitation training system including iontronic meta-fabrics withskin-friendly and large matrix features,as well as high-resolution image modules fordistribution of human muscle tension.Attributed to the dynamic connection and dissociationof the meta-fabric,the fabric exhibits outstanding tactile sensing properties,such as wide tactile sensing range(0~300 kPa)and high-resolution tactile perception(50 Pa or 0.058%).Meanwhile,thanks to the differential capillary effect,the meta-fabric exhibits a“hitting three birds with one stone”property(dryness wearing experience,long working time and cooling sensing).Based on this,the fabrics can be integrated with garmentsand advanced data analysis systems to manufacture a series of large matrix structure(40×40,1600 sensing units)training devices.Significantly,the tunability of piezo-ionic dynamics of the meta-fabric and the programmability of high-resolution imaging modules allowthis visualization training strategy extendable to various common disease monitoring.Therefore,we believe that our study overcomes theconstraint of standard spasticity rehabilitation training devices in terms of visual display and paves the way for future smart healthcare.
基金supported by the National Natural Science Foundation of China(Project U1901602&41790465)Key Special Project for Introduced Talents Team of Southern Marine Science and Engineering Guangdong Laboratory(Guangzhou)(GML2019ZD0203)+2 种基金Shenzhen Key Laboratory of Deep Offshore Oil and Gas Exploration Technology(Grant No.ZDSYS20190902093007855)Shenzhen Science and Technology Program(Grant No.KQTD20170810111725321)the leading talents of Guangdong province program(Grant No.2016LJ06N652).
文摘In 3D frequency domain seismic forward and inversion calculation,the huge amount of calculation and storage is one of the main factors that restrict the processing speed and calculation efficiency.The frequency domain finite-difference forward simulation algorithm based on the acoustic wave equation establishes a large bandwidth complex matrix according to the discretized acoustic wave equation,and then the frequency domain wave field value is obtained by solving the matrix equation.In this study,the predecessor's optimized five-point method is extended to a 3D seven-point finite-difference scheme,and then a perfectly matched layer absorbing boundary condition(PML)is added to establish the corresponding matrix equation.In order to solve the complex matrix,we transform it to the equivalent real number domain to expand the solvable range of the matrix,and establish two objective functions to transform the matrix solving problem into an optimization problem that can be solved using gradient methods,and then use conjugate gradient algorithm to solve the problem.Previous studies have shown that in the conjugate gradient algorithm,the product of the matrix and the vector is the main factor that affects the calculation efficiency.Therefore,this study proposes a method that transform bandwidth matrix and vector product problem into some equivalent vector and vector product algorithm,thereby reducing the amount of calculation and storage.
基金National Natural Science Foundation of China(10575070,10675081)Research Foundation Doctoral Program of Higher Education of China(20060248050)+1 种基金Scientific Research Foundation of Ministry of Education in China for Returned Scholars(NCET-07-0557)Major State Basic Research Development Program of China(2007CB815000)
文摘We recently performed a series of improvement on evaluation of eigenvalues without complicated iterations.In this work we first discuss evaluation of the lowest eigenvalue for given systems,by which one conveniently obtains the value of the lowest eigenvalue based on the dimension and width of given matrix.We also discuss a strong correlation between eigenvalues and diagonal matrix elements for large matrices,by which one is able to predict eigenvalues approximately without iterations.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10471074, 10771116)the Doctoral Program of the Ministry of Education of China (Grant No. 20060003003)
文摘The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, it is shown in this paper that under the original given condition the inexact RQI may not quadratically converge to the desired eigenpair and even may misconverge to some other undesired eigenpair. A new condition, called the uniform positiveness condition, is given that can fix misconvergence problem and ensure the quadratic convergence of the inexact RQI. An alternative to the inexact RQI is the Jacobi-Davidson (JD) method without subspace acceleration. A new proof of its linear convergence is presented and a sharper bound is established in the paper. All the results are verified and analyzed by numerical experiments.
文摘As is well known, solving matrix multiple eigenvalue problems is a very difficult topic. In this paper, Arnoldi type algorithms are proposed for large unsymmetric multiple eigenvalue problems when the matrix A involved is diagonalizable. The theoretical background is established, in which lower and upper error bounds for eigenvectors are new for both Arnoldi's method and a general perturbation problem, and furthermore these bounds are shown to be optimal and they generalize a classical perturbation bound due to W. Kahan in 1967 for A symmetric. The algorithms can adaptively determine the multiplicity of an eigenvalue and a basis of the associated eigenspace. Numerical experiments show reliability of the algorithms.
