This paper deals with the distributed solving problem of a specific class of linear algebraic equations(LAEs)with block Toeplitz structures.To reduce the communication burden and achieve computation efficiency,a distr...This paper deals with the distributed solving problem of a specific class of linear algebraic equations(LAEs)with block Toeplitz structures.To reduce the communication burden and achieve computation efficiency,a distributed iterative algorithm from the communication-efficient perspective is proposed by incorporating the specific structure of the coefficient matrix tied to any given LAE over a multi-agent network.Each agent possesses a state vector of size smaller than the dimensions of unknown variables related to the LAE and receives information from its neighbors.It is shown that the presented distributed iterative algorithm can solve the specific class of LAEs without requiring any initialization conditions,irrespective of whether it admits a unique solution or multiple solutions.Moreover,an equivalent relation is established between the problem of solving LAEs and the tracking problem of iterative learning control(ILC)systems.The proposed distributed iterative algorithm is leveraged to obtain the distributed control law for ILC systems to realize the tracking objective.Theoretical guarantees are provided for our developed solution results of LAEs,and the effectiveness of them is also verified through simulation examples.展开更多
In this paper, we study one kind of singular integral equations with singularity of order one. By the generalized Plemelj formula, this class of equations are transformed into a system of linear algebraic equations. I...In this paper, we study one kind of singular integral equations with singularity of order one. By the generalized Plemelj formula, this class of equations are transformed into a system of linear algebraic equations. In particular, we prove the existence of solution to the equation. The general solutions and the conditions of solvability are obtained in function class H.展开更多
An alternative method of solving Lagrange＇s first-order partial differential equation of the form（a1x ＋b1y＋C1z）p＋ （a2x ＋b2y＋c2z）q =a3x ＋b3y＋c3z,where p = Эz/Эx, q = Эz/Эy and ai, bi, ci （i = 1,2,3） a...An alternative method of solving Lagrange＇s first-order partial differential equation of the form（a1x ＋b1y＋C1z）p＋ （a2x ＋b2y＋c2z）q =a3x ＋b3y＋c3z,where p = Эz/Эx, q = Эz/Эy and ai, bi, ci （i = 1,2,3） are all real numbers has been presented here.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.U2333215,62273018,and U2133210。
文摘This paper deals with the distributed solving problem of a specific class of linear algebraic equations(LAEs)with block Toeplitz structures.To reduce the communication burden and achieve computation efficiency,a distributed iterative algorithm from the communication-efficient perspective is proposed by incorporating the specific structure of the coefficient matrix tied to any given LAE over a multi-agent network.Each agent possesses a state vector of size smaller than the dimensions of unknown variables related to the LAE and receives information from its neighbors.It is shown that the presented distributed iterative algorithm can solve the specific class of LAEs without requiring any initialization conditions,irrespective of whether it admits a unique solution or multiple solutions.Moreover,an equivalent relation is established between the problem of solving LAEs and the tracking problem of iterative learning control(ILC)systems.The proposed distributed iterative algorithm is leveraged to obtain the distributed control law for ILC systems to realize the tracking objective.Theoretical guarantees are provided for our developed solution results of LAEs,and the effectiveness of them is also verified through simulation examples.
基金Supported by the Qufu Normal University Youth Fund(XJ201218)
文摘In this paper, we study one kind of singular integral equations with singularity of order one. By the generalized Plemelj formula, this class of equations are transformed into a system of linear algebraic equations. In particular, we prove the existence of solution to the equation. The general solutions and the conditions of solvability are obtained in function class H.
文摘An alternative method of solving Lagrange＇s first-order partial differential equation of the form（a1x ＋b1y＋C1z）p＋ （a2x ＋b2y＋c2z）q =a3x ＋b3y＋c3z,where p = Эz/Эx, q = Эz/Эy and ai, bi, ci （i = 1,2,3） are all real numbers has been presented here.
